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Solution Manual for Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences, 14th Edition

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    I NSTRUCTOR A NSWERS F INITE M ATHEMATICS FOR B USINESS , E CONOMICS , L IFE S CIENCES , AND S OCIAL S CIENCES F OURTEENTH E DITION Raymond Barnett Merritt College Michael Ziegler Marquette University Karl Byleen Marquette University Christopher J. Stocker Marquette University

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    Diagnostic Prerequisite Test Section references are provided in parentheses following each answer to guide students to the specific content in the book where they can find help or remediation. 1. (A) ( y + z ) x (B) (2 + x ) + y (C) 2 x + 3 x (A.1) 2. x 3 - 3 x 2 + 4 x + 8 (A.2) 3. x 3 + 3 x 2 - 2 x + 12 (A.2) 4. - 3 x 5 + 2 x 3 - 24 x 2 + 16 (A.2) 5. (A) 1 (B) 1 (C) 2 (D) 3 (A.2) 6. (A) 3 (B) 1 (C) - 3 (D) 1 (A.2) 7. 14 x 2 - 30 x (A.2) 8. 6 x 2 - 5 xy - 4 y 2 (A.2) 9. 1 x + 2 21 x + 5 2 (A.3) 10. x 1 x + 3 21 x - 5 2 (A.3) 11. 7 > 20 (A.1) 12. 0.875 (A.1) 13. (A) 4.065 * 10 12 (B) 7.3 * 10 - 3 (A.5) 14. (A) 255,000,000 (B) 0,000 406 (A.5) 15. (A) T (B) F (A.1) 16. 0 and - 3 are two examples of infinitely many. (A.1) 17. 6 x 5 y 15 (A.5) 18. 3 u 4 > v 2 (A.5) 19. 6 * 10 2 (A.5) 20. x 6 / y 4 (A.5) 21. u 7 > 3 (A.6) 22. 3 a 2 > b (A.6) 23. 5 9 (A.5) 24. x + 2 x 1 > 2 y 1 > 2 + y (A.6) 25. a 2 + b 2 ab (A.4) 26. a 2 - c 2 abc (A.4) 27. y 5 x (A.4) 28. 1 xy 2 (A.4) 29. - 1 7(7 + h ) (A.4) 30. xy y - x (A.6) 31. (A) Subtraction (B) Commutative ( + ) (C) Distributive (D) Associative ( # ) (E) Negatives (F) Identity ( + ) (A.1) 32. (A) 6 (B) 0 (A.1) 33. 4 x = x - 4; x = - 4 > 3 (1.1) 34. - 15 > 7 (1-2) 35. (4/7, 0) (1.2) 36. (0, - 4) (1-2) 37. x = 0, 5 (A.7) 38. x = { 1 7 (A.7) 39. x = - 4, 5 (A.7) 40. x = 1, 1 6 (A.7) A-1 ANSWERS

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    (B) x int.: 6.5; y int.: 5.2 (C) 10 2 10 10 2 10 (D) x int.: 6.5; y int.: 5.2 Chapter 1 Exercises 1.1 1. x = 5 2. x = - 9 3. x = 2 4. x = - 3 5. x = - 19 6. x = - 2 7. 4 … x 6 13 8. - 3 6 x … 5 9. - 2 6 x 6 7 10. - 6 … x … - 1 11. x … 4 12. x Ú 9 13. 1 - 8, 2 4 14. 3 - 1, 5 2 15. 1 - ∞ , 9 2 16. 3 4, ∞ 2 17. 1 - 7, - 5 4 18. 3 - 3, 2 2 19. x = - 3 2 20. m = 14 21. y 6 - 15 2 22. x 7 - 10 3 23. u = - 3 4 24. y = 2 3 25. x = 10 26. x = 4 27. y Ú 3 28. x … 8 29. x = 36 30. y = - 6 31. m 6 36 7 32. u 6 16 33. 3 … x 6 7 or 3 3, 7 2 3 7 x 34. - 2 … x 6 3 or 3 - 2, 3 2 2 2 3 x 35. - 20 … C … 20 or 3 - 20, 20 4 20 x 2 20 36. - 9 … t … 9 or 3 - 9, 9 4 9 t 2 9 37. y = 3 4 x - 3 38. x = - 3 2 y + 1 2 39. y = - 1 A > B 2 x + 1 C > B 2 = 1 - Ax + C 2 > B 40. m = y - b x 41. C = 5 9 1 F - 32 2 42. F = 9 5 C + 32 43. - 2 6 x … 1 or 1 - 2, 1 4 1 2 2 x 44. 14 3 … u … 6 or c 14 3 , 6 d 6 u 14 3 45. Negative 46. Positive 47. 4,500 $35 tickets and 5,000 $55 tickets 48. 30 quarters; 70 dimes 49. Fund A: $180,000; Fund B: $320,000 50. Fund A: $340,000; Fund B: $160,000 51. $15,405 52. $24,493 53. (A) $420 (B) $55 54. (A) $51 (B) $160 55. 34 rounds 56. 12 times 57. $32,000 58. (A) $20,000 (B) $24,493 (C) Choose the payment method with the larger base salary unless you can sell more than $52,000 per month. 59. 5,851 books 60. 7,132 books 61. (B) 6,180 books (C) At least $11.50 62. (B) 7,480 books (C) At least $15.60 63. 5,000 64. - 45 … C … - 10 65. 12.6 yr 66. 9.6 to 16.8 Exercises 1.2 1. (D) 2. (A) 3. (C) 4. (B) 5. y 5 5 x 6. y 5 5 x 7. y 3 6 x 8. y 1 5 x 9. Slope = 5; y int. = - 7 10. Slope = 3; y int. = 2 11. Slope = - 5 2 ; y int. = - 9 12. Slope = - 10 3 ; y int. = 4 13. S lope = 1 4 ; y int. = 2 3 14. S lope = 1 5 ; y int. = - 1 2 15. Slope = 2; x int. = - 5 16. Slope = - 4; x int. = 3 17. Slope = 8; x int. = 5 18. Slope = - 3; x int. = 2 19. S lope = 6 7 ; x int. = - 7 20. S lope = - 9 2 ; x int. = 4 9 21. y = 2 x + 1 22. y = x + 5 23. y = - 1 3 x + 6 24. y = 6 7 x - 9 2 25. x int.: 1 2 ; y int.: 1; y = - 2 x + 1 26. x int.: 1; y int.: 3; y = - 3 x + 3 27. x int.: - 3; y int.:1; y = x 3 + 1 28. x int.: 2; y int.: - 1; y = x 2 - 1 29. y 5 5 x 30. y 5 5 x 31. (D) x int.: 3.5; y int.: - 4.2 y 5 5 x 32. y 5 5 x 33. y 5 5 x y 5 2 2 x 5 3 34. y 5 5 x y 5 2 x 5 2 3 35. - 4 36. 5 37. - 3 5 38. 2 3 39. 2 40. 1 8 41. (A) (B) (C) y 10 10 x 42. (A) (B) (C) y 6 10 x 43. y x 3,0 00 100 44. y x 5,0 00 4,000 3,000 2,000 1,000 100 20 0 60 45. (A) y 10 10 x (B) x int.: 3.5; y int.: - 4.2 (C) 10 2 10 10 2 10 46. (A) y 10 6 x ANSWERS A-2

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    Answers A-3 86. (A) p = 0.0005 x - 1.7 (B) p = - 0.0005 x + 7.8 (C) (9,500, 3.05) (D) p x 3.20 3.00 2.80 9,800 Supply Demand 9,200 0 Dollars Millions of Bushels Equilibrium point 47. x = 4, y = - 3 48. x = - 5; y = 6 49. x = - 1.5, y = - 3.5 50. x = 2.6; y = 3.8 51. y = 5 x - 15 52. y = 4 x + 6 53. y = - 2 x + 7 54. y = - 10 x + 15 55. y = 1 3 x - 20 3 56. y = 2 7 x - 1 57. y = - 3.2 x + 30.86 58. y = 0.9 x + 4.63 59. (A) m = 2 3 (B) - 2 x + 3 y = 11 (C) y = 2 3 x + 11 3 60. (A) m = 3 2 (B) 3 x - 2 y = - 1 (C) y = 3 2 x + 1 2 61. (A) m = - 5 4 (B) 5 x + 4 y = - 14 (C) y = - 5 4 x - 7 2 62. (A) m = - 4 5 (B) 4 x + 5 y = 23 (C) y = - 4 5 x + 23 5 63. (A) Not defined (B) x = 5 (C) None 65. (A) m = 0 (B) y = 5 (C) y = 5 66. (A) Not defined (B) x = 2 (C) None 67. The graphs have the same y int., (0, 2). 68. The graphs have the same slope, - 0.5. 69. C = 124 + 0.12 x ; 1,050 donuts 70. C = 1,200 + 45 x ; 80 picnic tables 71. (A) C = 75 x + 1,647 (B) C x 5,000 10,000 15,000 0 0 5 0 5 1 0 0 1 (C) The y int., $1,647, is the fixed cost and the slope, $75, is the cost per club. 72. (A) C = 39 x + 1,905 (B) C x 6,0 00 4,000 2,000 100 20 0 60 (C) The y int., $1,905, is the fixed cost, and the slope, $39, is the cost per racket. 73. (A) R = 1.4 C - 7 (B) $137 74. (A) R = 1.5 C + 3 (B) $158 75. (A) V = - 7,500 t + 157,000 (B) $112,000 (C) During the 12th year (D) V t $40,000 $80,000 $120,000 10 0 20 Years (6, 112,000) (11.6, 70,000) 76. (A) V = - 6,800 t + 224,000 (B) $156,000 (C) During the 19th year (D) V t $40,000 $80,000 $120,000 $160,000 $200,000 10 0 20 Years (10, 156,000) (18.24, 100,000) 77. (A) T = - 1.84 x + 212 (B) 205.56°F (C) 6,522 ft (D) T x 220 180 190 200 210 20 10 0 Temperature ( 8 F) Thousands of Feet (3.5, 205.56) (6.522, 200) 78. (A) T = 14 x - 206.6 (B) 227.4°F (C) 28.97 inHg (D) T x 225 215 205 195 185 32 28 30 0 Temperature ( 8 F) Barometric Pressure (inHg) (31, 227.4) (28.97, 199) 79. (A) T = 70 - 3.6 A (B) 10,000 ft 80. (A) T = 3.2 A + 200 (B) 220.8 mph 81. (A) N = - 0.0063 t + 2.76 (B) 2.45 persons 82. (A) I = 1,031 t + 30,000 (B) $71,240 83. (A) f = - 0.49 t + 21 (B) 2028 84. (A) m = - 0.6 t + 25.7 (B) 2031 85. (A) p = 0.001 x + 5.4 (B) p = - 0.001 x + 13 (C) (3,800, 9.2) (D) p x 10 9.5 9 4,200 0 0 0 4 , 3 Dollars Equilibrium point Demand Supply 87. (A) s = 2 5 w (B) 8 in. (C) 9 lb Exercises 1.3 1. (A) w = 49 + 1.7 h (B) The rate of change of weight with respect to height is 1.7 kg/in. (C) 55.8 kg (D) 5 ′ 6.5 ″ 2. (A) w = 52 + 1.9 h (B) The rate of change of weight with respect to height is 1.9 in./kg. (C) 67.2 kg (D) 5 ′ 9.5 ″ 3. (A) P = 0.445 d + 14.7 (B) The rate of change of pressure with respect to depth is 0.445 lb/in. 2 per ft. (C) 37 lb/in. 2 (D) 99 ft 4. (A) P = 0.43 d + 14.7 (B) The rate of change of pressure with respect to depth is 0.43 lb/in.2 per ft. (C) 36.3 lb/in.2 (D) 102 ft 5. (A) a = 2,880 - 24 t (B) - 24 ft/sec (C) 24 ft/sec 6. (A) a = - 16 t + 2,880 (B) - 16 ft/sec (C) 16 ft/sec 7. s = 0.6 t + 331 ; the rate of change of the speed of sound with respect to temperature is 0.6 m/s per °C. 8. x = 3.9 t + 1,403; the rate of change of the speed of sound with respect to temperature is 3.9 m/s per °C. 9. (A) y x 100 80 60 40 20 25 30 5 0 10 15 20 U.S. Fossil Fuel Production (%) Years since 1985 (B) The rate of change of fossil fuel production is - 0.19 % per year. (C) 76% of total production (D) 2058 10. (A) y x 100 80 60 40 20 25 30 5 0 10 15 20 U.S. Fossil Fuel Consumption (%) Years since 1985 (B) The rate of change of fossil fuel consumption is - 0.14% per year. (C) 81% (D) 2030 11. (A) f t 25 20 15 10 5 15 18 3 0 6 9 12 Female Smokers (%) Years since 1997 12. (A) m t 25 20 15 10 5 15 18 3 0 6 9 12 Male Smokers (%) Years since 1997 13. (A) y x 1 0.5 1 0.5 0 Licensed Drivers (millions) Population (millions) (B) 1,050,000 (C) 1,359,000 (B) 2025 (B) 2029 14. (A) y x 40 20 40 20 0 Licensed Drivers (millions) Population (millions) (B) 6,428,000 (C) 10,339,000 15. (A) S t 600 300 20 10 0 Net Sales (millions) Years since 2000 (B) $662 billion 88. (A) d = - 4 w + 30 (B) 30 in. (C) 7.5 lb

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    A-4 Answers 17. (A) y x 24 80 30 2 30 2 60 0 Ethylene Glycol (%wt) Degrees ( 8 F) (B) 2°F (C) 22.75% 18. (A) y x 30 60 90 30 30 60 0 Propylene Glycol (%wt) Degrees ( F) (B) 7°F (C) 25.9% 19. (A) The rate of change of height with respect to Dbh is 1.37 ft/in. (B) Height increases by approximately 1.37 ft. (C) 18 ft (D) 20 in. 20. (A) The rate of change of height with respect to Dbh is 1.66 ft/in. (B) Height increases by approximately 1.66 ft. (C) 15 ft (D) 18 in. 21. (A) Undergraduate male enrollment is increasing at a rate of 87,000 students per year; undergraduate female enrollment is increasing at a rate of 140,000 students per year. (B) Male: 8.6 million; female: 11.5 million (C) 2026 22. (A) Graduate male enrollment is increasing at a rate of 11,000 students per year; graduate female enrollment is increasing at a rate of 31,000 students per year. (B) Male: 1.3 million; female: 2.1 million (C) 2037 23. y = 0.061 x + 50.703 ; 54.67 ° F 24. y = 0.051 x + 30.166; 33.48 in. 25. Men: y = - 0.070 x + 49.058; women: y = - 0.085 x + 54.858; yes 26. Men: y = - 0.247 x + 119.097; Women: y = - 0.122 x + 128.494; no 27. Supply: y = 0.2 x + 0.87; demand: y = - 0.15 x + 3.5; equilibrium price = $2.37 28. Supply: y = 1.53 x + 2.85; demand: y = - 2.21 x + 10.66; equilibrium price: $6.05 Chapter 1 Review Exercises 1. x = 2.8 (1.1) 2. x = 2 (1.1) 3. y = 1.8 - 0.4 x (1.1) 4. x = 4 3 y + 7 3 (1.1) 5. y 6 13 4 or a - ∞ , 13 4 b y 13 4 (1.1) 6. 1 … x 6 3 or [1, 3) 1 3 x (1.1) 7. x Ú 9 2 or c 9 2 , ∞ b 9 2 x (1.1) 8. y 4 5 x (1.2) 9. 2 x + 3 y = 12 (1.2) 10. x int. = 9; y int. = - 6; slope = 2 3 (1.2) y 10 10 x 11. y = - 2 3 x + 6 (1.2) 16. (A) I t 40 20 0 0 1 0 2 Operating Income (millions) Years since 2000 (B) $37.2 billion 21. x Ú 1 or [1, ∞ ) (1.1) 1 x 22. x 6 - 143 17 or a - ∞ , - 143 17 b 143 17 2 x (1.1) 23. 1 6 x … 4 or (1, 4 4 4 1 x (1.1) 24. 3 8 … x … 7 8 or c 3 8 , 7 8 d x 7 8 3 8 (1.1) 25. (A) (B) (C) y 10 10 x (1.2) 26. The graph of x = - 3 is a vert. line with x int. - 3, and the graph of y = 2 is a hor. line with y int. 2. (1.2) y x 5 5 27. (A) An oblique line through the origin with slope - 3 4 (B) A vert. line with x int. - 4 3 (C) The x axis (D) An oblique line with x int. 12 and y int. 9 (1.2) 28. 2 A - bh h (1.1) 29. S - P St (1.1) 30. a 6 0 and b any real number (1.1) 31. Less than (1.1) 32. The graphs appear to be perpendicular to each other. (It can be shown that if the slopes of two slant lines are the negative reciprocals of each other, then the two lines are perpendicular.) (1.2) 33. $75,000 (1.1) 34. 9,375 DVDs (1.1) 35. (A) m = 132 - 0.6 x (B) M = 187 - 0.85 x (C) Between 120 and 170 beats per minute (D) Between 102 and 144.5 beats per minute (1.3) 36. (A) V = 224,000 - 15,500 t (B) $38,000 (1.2) 37. (A) R = 1.6 C (B) $192 (C) $110 (D) The slope is 1.6. This is the rate of change of retail price with respect to cost. (1.2) 38. $400; $800 (1.1) 39. Demand: p = 5.24 - 0.00125 x ; 1,560 bottles (1.2) 40. (A) T M 40 120 80 40 0 48 60 12 (B) - 30 ° F (C) 45% (1.3) 41. (A) The dropout rate is decreasing at a rate of 0.308 percentage points per year. (B) r t 20 10 0 0 2 0 4 Dropout Rate (%) Years since 1990 (C) 2026 (1.3) 42. (A) The CPI is increasing at a rate of 4.295 units per year. (B) 276.62 (1.3) 43. (A) The rate of change of tree height with respect to Dbh is 0.74. (B) Tree height increases by about 0.74 ft. (C) 21 ft (D) 16 in. (1.3) 12. Vert. line: x = - 6; hor. line: y = 5 (1.2) 13. (A) y = - 2 3 x (B) y = 3 (1.2) 14. (A) 3 x + 2 y = 1 (B) y = 5 (C) x = - 2 (1.2) 15. x = 25 2 (1.1) 16. u = 36 (1.1) 17. x = 30 11 (1.1) 18. x = 21 (1.1) 19. x = 4 (1.1) 20. x 6 4 or 1 - ∞ , 4 2 (1.1) 4 x

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    Chapter 2 Exercises 2.1 1. y x 5 5 2. y x 5 5 3. y x 5 10 4. y x 10 5 5. y x 50 5 6. y x 5 50 7. y x 4 3 8. y x 10 10 9. A function 10. A function 11. Not a function 12. Not a function 13. A function 14. A function 15. A function 16. A function 17. Not a function 18. Not a function 19. A function 20. Not a function 21. Linear 22. Neither 23. Neither 24. Linear 25. Linear 26. Neither 27. Constant 28. Constant 29. y x 5 5 30. y x 5 3 31. y x 10 5 32. y x 10 5 33. y x 50 5 34. y x 50 5 35. y x 10 10 36. y x 4 4 37. y x 5 5 38. y 5 5 x 39. y = 0 40. y = 0 41. y = 4 42. y = 3 43. x = - 5 44. x = 5 45. x = - 6 46. x = - 5 , 0, 4 47. All real numbers 48. All real numbers 49. All real numbers except - 4 50. All real numbers except 2 51. x … 7 52. x 7 - 5 53. Yes; all real numbers 54. Yes; all real numbers 55. No; for example, when x = 0, y = { 2 56. Yes; all real numbers except 0 57. Yes; all real numbers except 0 58. No; when x = 0, y = { 3 59. No; when x = 1, y = { 1 60. Yes; x Ú 0 61. 25 x 2 - 4 62. 9 x 2 - 4 63. x 2 + 4 x 64. x 2 - 2 x - 3 65. x 4 - 4 66. x 6 - 4 67. x - 4 68. 1 x - 4 69. h 2 - 4 70. h 2 + 1 71. 4 h + h 2 72. 5 - 6 h + h 2 73. 4 h + h 2 74. - 6 h + h 2 75. (A) 4 x + 4 h - 3 (B) 4 h (C) 4 76. (A) - 3 x - 3 h + 9 (B) - 3 h (C) - 3 77. (A) 4 x 2 + 8 xh + 4 h 2 - 7 x - 7 h + 6 (B) 8 xh + 4 h 2 - 7 h (C) 8 x + 4 h - 7 78. (A) 3 x 2 + 6 xh + 3 h 2 + 5 x + 5 h - 8 (B) 6 xh + 3 h 2 + 5 h (C) 6 x + 3 h + 5 79. (A) 20 x + 20 h - x 2 - 2 xh - h 2 (B) 20 h - 2 xh - h 2 (C) 20 - 2 x - h 80. (A) x 2 + 2 xh + h 2 + 40 x + 40 h (B) 2 xh + h 2 + 40 h (C) 2 x + h + 40 81. P 1 w 2 = 2 w + 50 w , w 7 0 82. P 1 l 2 = 2 l + 162 l , l 7 0 83. A 1 l 2 = l 1 50 - l 2 , 0 6 l 6 50 84. A 1 w 2 = 1 80 - w 2 w , 0 6 w 6 80 86. (A) p x $2,0 00 25 (B) $54; $42 (B) $1,340; $920 87. (A) R 1 x 2 = 1 75 - 3 x 2 x , 1 … x … 20 (B) x R(x) 1 72 4 252 8 408 12 468 16 432 20 300 (C) R ( x ) x $500 20 88. (A) R 1 x 2 = x 1 2,000 - 60 x 2 , 1 … x … 25 (B) x R ( x ) 1 1,940 5 8,500 10 14,000 15 16,500 20 16,000 25 12,500 (C) R ( x ) x $15,0 00 25 89. (A) P 1 x 2 = 59 x - 3 x 2 - 125, 1 … x … 20 (B) x P(x) 1 - 69 4 63 8 155 12 151 16 51 20 - 145 (C) P ( x ) $200 2 200 x 15 90. (A) P 1 x 2 = 1,500 x - 60 x 2 - 4,000, 1 … x … 25 (B) x P ( x ) 1 - 2,560 5 2,000 10 5,000 15 5,000 20 2,000 25 - 4,000 (C) P ( x ) x 25 $5,000 91. v = 75 - w 15 + w ; 1.9032 cm/sec 92. (A) v = 0.4 s + 0.28; 48.4% (B) s = 2.5 v - 0.7; 57.5% ANSWERS 85. (A) p ( x ) x $10 0 20 Exercises 2.2 1. Domain: all real numbers; range: [ - 4, ∞ ] 2. Domain: 3 0, ∞ 2 ; range: 3 1, ∞ 2 3. Domain: all real numbers; range: all real numbers 4. Domain: all real numbers; range: 3 10, ∞ 2 5. Domain: [0, ∞ 2 ; range: 1 - ∞ , 8] 6. Domain: all real numbers; range: all real numbers 7. Domain: all real numbers; range: all real numbers 8. Domain: all real numbers; range: 1 - ∞ , 15] 9. Domain: all real numbers; range: [9, ∞ 2 10. Domain: all real numbers; range: all real numbers 11. x 5 5 12. x 5 5 13. x 5 5 A-5

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    A-6 Answers 28. The graph of h 1 x 2 = - 0 x - 5 0 is the graph of y = 0 x 0 reflected in the x axis and shifted 5 units to the right. h ( x ) x 10 10 29. The graph of f 1 x 2 = 1 x - 4 2 2 - 3 is the graph of y = x 2 shifted 4 units to the right and 3 units down. f ( x ) x 10 10 30. The graph of m 1 x 2 = 1 x + 3 2 2 + 4 is the graph of y = x 2 shifted 3 units to the left and 4 units up. x 10 10 m ( x ) 31. The graph of f 1 x 2 = 7 - 1 x is the graph of y = 1 x reflected in the x axis and shifted 7 units up. f ( x ) x 10 10 32. The graph of g 1 x 2 = - 6 + 1 3 x is the graph of y = 1 3 x shifted 6 units down. x 10 10 g ( x ) 44. g 1 x 2 = 1 3 x + 3 + 2 g ( x ) x 5 5 45. g 1 x 2 = -  x + 3  g ( x ) x 5 5 46. g 1 x 2 = - 0 x - 1 0 g ( x ) x 5 5 47. g 1 x 2 = - 1 x - 2 2 3 - 1 g ( x ) x 5 5 48. g 1 x 2 = 4 - 1 x + 2 2 2 g ( x ) x 5 5 49. f ( x ) x 5 5 50. g ( x ) x 5 5 51. h ( x ) x 30 20 52. h ( x ) x 60 40 53. h ( x ) x 100 80 54. h ( x ) x 300 200 55. The graph of the basic function y =  x  is reflected in the x axis and vertically shrunk by a factor of 0.5. Equation: y = - 0.5  x  . 14. x 5 5 15. x 5 2 16. x 5 5 17. x 5 5 18. x 5 5 19. x 5 5 20. x 5 5 21. x 5 5 22. x 5 5 23. x 5 5 24. x 5 5 25. x 5 5 26. x 5 5 27. The graph of g 1 x 2 = -  x + 3  is the graph of y =  x  reflected in the x axis and shifted 3 units to the left. g ( x ) x 10 10 33. The graph of h 1 x 2 = - 3  x  is the graph of y =  x  reflected in the x axis and vertically stretched by a factor of 3. h ( x ) x 10 10 34. The graph of m 1 x 2 = - 0.4 x 2 is the graph of y = x 2 reflected in the x axis and vertically shrunk by a factor of 0.4. x 10 10 m ( x ) 35. The graph of the basic function y = x 2 is shifted 2 units to the left and 3 units down. Equation: y = 1 x + 2 2 2 - 3. 36. The graph of the basic function y = 0 x 0 is shifted 3 units to the right and 2 units up. Equation: y = 0 x - 3 0 + 2. 37. The graph of the basic function y = x 2 is reflected in the x axis and shifted 3 units to the right and 2 units up. Equation: y = 2 - 1 x - 3 2 2 . 38. The graph of the basic function y = 0 x 0 is reflected in the x axis, shifted 2 units to the left and 3 units up. Equation: y = 3 - 0 x + 2 0 . 39. The graph of the basic function y = 1 x is reflected in the x axis and shifted 4 units up. Equation: y = 4 - 1 x . 40. The graph of the basic function 1 3 x is reflected in the x axis and shifted 2 units up. Equation: y = 2 - 1 3 x . 41. The graph of the basic function y = x 3 is shifted 2 units to the left and 1 unit down. Equation: y = 1 x + 2 2 3 - 1. 42. The graph of the basic function y = x 3 is reflected in the x axis, shifted 3 units to the right and 1 unit up. Equation: y = 1 - 1 x - 3 2 3 . 43. g 1 x 2 = 1 x - 2 - 3 g ( x ) x 5 5

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    Answers A-7 56. The graph of the basic function y = x is reflected in the x axis and vertically stretched by a factor of 2. Equation: y = - 2 x . 57. The graph of the basic function y = x 2 is reflected in the x axis and vertically stretched by a factor of 2. Equation: y = - 2 x 2 . 58. The graph of the basic function y = 0 x 0 is vertically stretched by a factor of 4. Equation: y = 4 0 x 0 . 59. The graph of the basic function y = 2 3 x is reflected in the x axis and vertically stretched by a factor of 3. Equation: y = - 3 2 3 x . 60. The graph of the basic function y = x 3 is vertically shrunk by a factor of 0.25. Equation: y = 0.25 x 3 . 61. Reversing the order does not change the result. 62. Reversing the order does not change the result. 63. Reversing the order can change the result. 64. Reversing the order can change the result. 65. Reversing the order can change the result. 66. Reversing the order does not change the result. 67. (A) The graph of the basic function y = 1 x is reflected in the x axis, vertically expanded by a factor of 4, and shifted up 115 units. (B) p ( x ) x $100 $50 100 0 200 68. (A) The graph of the basic function y = 1 x is vertically expanded by a factor of 4. (B) p ( x ) x 100 50 200 100 0 69. (A) The graph of the basic function y = x 3 is vertically contracted by a factor of 0.000 48 and shifted right 500 units and up 60,000 units. (B) C ( x ) x $10 0,000 $50,000 500 0 1000 70. (A) The graph of the basic function y = x 2 is reflected in the x axis, vertically contracted by a factor of 0.013, and shifted 10 units to the right and 190 units up. (B) p ( x ) x 250 50 100 150 200 100 50 0 71. (A) S 1 x 2 = e 8.5 + 0.065 x if 0 … x … 700 - 9 + 0.09 x if x 7 700 (B) S ( x ) x 100 1,400 72. (A) W 1 x 2 = e 8.5 + 0.065 x if 0 … x … 700 16.9 + 0.053 x if x 7 700 f (B) W x 10 0 1300 73. (A) T 1 x 2 = • 0.02 x if 0 6 x … 25,000 0.04 x - 500 if 25,000 6 x … 100,000 0.06 x - 2,500 if x 7 100,000 (B) T ( x ) x 3,0 00 100,000 (C) $1,700; $4,100 74. (A) T 1 x 2 = • 0.02 x if 0 … x 6 12,500 0.04 x - 250 if 12,500 6 x … 50,000 0.06 x - 1,250 if x 7 50,000 (B) T ( x ) x 1,50 0 50,000 (C) $1,030; $2,590 75. (A) The graph of the basic function y = x is vertically stretched by a factor of 5.5 and shifted down 220 units. (B) w ( x ) x 200 250 50 100 150 50 0 100 76. (A) The graph of the basic function y = x 3 is vertically stretched by a factor of 463. (B) w ( x ) x 250 50 100 150 200 1 0.5 0 77. (A) The graph of the basic function y = 1 x is vertically stretched by a factor of 7.08. (B) v ( x ) x 100 50 50 0 100 78. (A) The graph of the basic function y = 1 3 x is reflected in the x axis and shifted up 10 units. (B) T ( x ) x 10 5 125 25 50 75 0 Exercises 2.3 1. f 1 x 2 = 1 x - 5 2 2 - 25 2. f 1 x 2 = 1 x + 8 2 2 - 64 3. f 1 x 2 = 1 x + 10 2 2 - 50 4. f 1 x 2 = 1 x - 6 2 2 - 44 5. f 1 x 2 = - 2 1 x - 1 2 2 - 3 6. f 1 x 2 = 3 1 x + 3 2 2 - 6 7. f 1 x 2 = 2 a x + 1 2 b 2 + 1 2 8. f 1 x 2 = - 5 a x - 3 2 b 2 + 1 4 9. The graph of f 1 x 2 is the graph of y = x 2 shifted right 2 units and down 1 unit. 10. The graph of g 1 x 2 is the graph of y = x 2 shifted right 1 unit and down 6 units. 11. The graph of m 1 x 2 is the graph of y = x 2 reflected in the x axis, then shifted right 3 units and up 5 units. 12. The graph of n 1 x 2 is the graph of y = x 2 reflected in the x axis, then shifted right 4 units and up 7 units. 13. (A) m (B) g (C) f (D) n 14. (A) g (B) m (C) n (D) f 15. (A) x int.: 1, 3; y int.: - 3 (B) Vertex: (2, 1) (C) Max.: 1 (D) Range: y … 1 or 1 - ∞ , 1 4 16. (A) x int.: - 5, - 1; y int.: - 5 (B) Vertex: 1 - 3, 4 2 (C) max.: 4 (D) Range: y … 4 or 1 - ∞ , 4 4 17. (A) x int.: - 3, - 1; y int.: 3 (B) Vertex: 1 - 2, - 1 2 (C) Min.: - 1 (D) Range: y Ú - 1 or 3 - 1, ∞ 2 18. (A) x int.: 1, 5; y int.: 5 (B) Vertex: 1 3, - 4 2 (C) min.: - 4 (D) Range: y Ú - 4 or 3 - 4, ∞ 2 19. (A) x int.: 3 { 1 2; y int.: - 7 (B) Vertex: 1 3, 2 2 (C) Max.: 2 (D) Range: y … 2 or 1 - ∞ , 2 4 20. (A) x int.: - 2 { 1 3; y int.: - 1 (B) Vertex: 1 - 2, 3 2 (C) max.: 3 (D) Range: y … 3 or 1 - ∞ , 3 4 21. (A) x int.: - 1 { 1 2; y int.: - 1 (B) Vertex: 1 - 1, - 2 2 (C) Min.: - 2 (D) Range: y Ú - 2 or 3 - 2, ∞ 2 22. (A) x int.: 4 { 1 3; y int.: 13 (B) Vertex: 1 4, - 3 2 (C) min.: - 3 (D) Range: y Ú - 3 or 3 - 3, ∞ 2 23. y = - 3 x - 1 - 2 24 2 + 5 or y = - 1 x + 2 2 2 + 5 24. y = - 1 x - 4 2 2 + 2 25. y = 1 x - 1 2 2 - 3 26. y = 3 x - 1 - 3 24 2 + 1 or y = 1 x + 3 2 2 + 1 27. Vertex form: 1 x - 4 2 2 - 4 (A) x int.: 2, 6;

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    A-8 Answers y int.: 12 (B) Vertex: 1 4, - 4 2 (C) Min.: - 4 (D) Range: y Ú - 4 or 3 - 4, ∞ 2 28. Vertex form: 1 x - 3 2 2 - 4 (A) x int.: 1, 5; y int.: 5 (B) Vertex: 1 3, - 4 2 (C) min.: - 4 (D) Range: y Ú - 4 or 3 - 4, ∞ 2 29. Vertex form: - 4 1 x - 2 2 2 + 1 (A) x int.: 1.5, 2.5; y int.: - 15 (B) Vertex: 1 2, 1 2 (C) Max.: 1 (D) Range: y … 1 or 1 - ∞ , 1 4 30. Vertex form: - 4 1 x + 1 2 2 + 1 (A) x int.: - 3 2 , - 1 2 ; y int.: - 3 (B) Vertex: 1 - 1, 1 2 (C) max.: 1 (D) Range: y … 1 or 1 - ∞ , 1 4 31. Vertex form: 0.5 1 x - 2 2 2 + 3 (A) x int.: none; y int.: 5 (B) Vertex: 1 2, 3 2 (C) Min.: 3 (D) Range: y Ú 3 or 3 3, ∞ 2 32. Vertex form: 0.5 1 x + 4 2 2 + 2 (A) x int.: none; y int.: 10 (B) Vertex: 1 - 4, 2 2 (C) min.: 2 (D) Range: y Ú 2 or 3 2, ∞ 2 33. (A) - 4.87, 8.21 (B) - 3.44, 6.78 (C) No solution 34. (A) - 1.53, 6.53 (B) 0.36, 4.64 (C) No solution 35. 651.0417 36. 347.1429 37. g 1 x 2 = 0.25 1 x - 3 2 2 - 9.25 (A) x int.: - 3.08, 9.08; y int.: - 7 (B) Vertex: 1 3, - 9.25 2 (C) Min.: - 9.25 (D) Range: y Ú - 9.25 or 3 - 9.25, ∞ 2 38. m 1 x 2 = 0.20 1 x - 4 2 2 - 4.2 (A) x int.: - 0.58, 8.58; y int.: - 1 (B) Vertex: 1 4, - 4.2 2 (C) min.: - 4.2 (D) Range: y Ú - 4.2 or 3 - 4.2, ∞ 2 39. f 1 x 2 = - 0.12 1 x - 4 2 2 + 3.12 (A) x int.: - 1.1, 9.1; y int.: 1.2 (B) Vertex: 1 4, 3.12 2 (C) Max.: 3.12 (D) Range: y … 3.12 or 1 - ∞ , 3.12 4 40. n 1 x 2 = - 0.15 1 x + 3 2 2 + 4.65 (A) x int.: - 8.57, 2.57; y int.: 3.30 (B) Vertex: 1 - 3, 4.65 2 (C) max.: 4.65 (D) Range: y … 4.65 or 1 - ∞ , 4.65 4 41. 1 - ∞ , - 5 2 h 1 3, ∞ 2 42. 1 - 6, 3 2 43. 3 - 3, 2 4 44. 1 - ∞ , - 4 4 ∪ 3 - 3, ∞ 2 45. x = - 5.37, 0.37 46. x = - 1.27, 2.77 47. - 1.37 6 x 6 2.16 48. - 0.88 … x … 3.52 49. x … - 0.74 or x Ú 4.19 50. x 6 - 1 or x 7 2.72 51. Axis: x = 2; vertex: (2, 4); range: y Ú 4 or 3 4, ∞ 2 ; no x int. 52. Axis: x = - 3; vertex: 1 - 3, - 5 2 ; range: y … - 5 or 1 - ∞ , - 5]; no x intercept 53. (A) y x g f 15 10 (B) 1.64, 7.61 (C) 1.64 6 x 6 7.61 (D) 0 … x 6 1.64 or 7.61 6 x … 10 54. (A) y x g f 10 7 (B) 0.93, 5.35 (C) 0.93 6 x 6 5.35 (D) 0 … x 6 0.93 or 5.35 6 x … 7 55. (A) y x 15 10 g f (B) 1.10, 5.57 (C) 1.10 6 x 6 5.57 (D) 0 … x 6 1.10 or 5.57 6 x … 8 56. (A) y x g f 15 10 (B) 1.08, 6.35 (C) 1.08 6 x 6 6.35 (D) 0 … x 6 1.08 or 6.35 6 x … 9 65. (A) x 28 30 32 34 36 Mileage 45 52 55 51 47 f ( x ) 45.3 51.8 54.2 52.4 46.5 (B) y x 50 40 30 20 10 36 28 0 32 (C) f 1 31 2 = 53.50 thousand miles; (D) f 1 35 2 = 49.95 thousand miles; 69. (A) R ( x ) x 500 20 (B) 12.5 (12,500,000 chips); $468,750,000 (C) $37.50 70. (A) R x 16,0 00 25 (B) 16.667 (16,667 computers); $16,667,000 (C) $1,000 71. (A) y x 50 0 20 C R (B) 2,415,000 chips and 17,251,000 chips (C) Loss: 1 … x 6 2.415 or 17.251 6 x … 20; profit: 2.415 6 x 6 17.251 72. (A) y R C x 16,0 00 25 (B) 3,035 computers and 21,965 computers (C) Loss: 1 … x 6 3.035 or 21.965 6 x … 25; profit: 3.035 6 x 6 21.965 73. (A) P 1 x 2 = 59 x - 3 x 2 - 125 C R P y x 500 2 200 15 (C) Intercepts and break-even points: 2,415,000 chips and 17,251,000 chips (D) Maximum profit is $165,083,000 at a production level of 9,833,000 chips. This is much smaller than the maximum revenue of $468,750,000. 74. (A) P 1 x 2 = 1,500 x - 60 x 2 - 4,000 y R P C x 16,0 00 25 (C) Intercepts and break-even points: 3,035 computers and 21,965 computers (D) Maximum profit is $5,375,000 at a production level of 12,500 computers. This is much smaller than the maximum revenue of $16,666,667. 75. x = 0.14 cm 76. x = 0.10 cm 77. 10.6 mph 78. 5.6 mpg 66. (A) x 5 10 15 20 25 30 35 Market share 18.8 20.0 20.7 20.2 17.4 16.4 15.3 f ( x ) 19.2 19.9 20.1 19.6 18.6 17.0 14.8 (B) y x 20 35 (C) f 1 45 2 = 8.6%; f 1 48 2 = 6.3%

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    Answers A-9 Exercises 2.4 1. (A) 1 (B) - 3 (C) 21 2. (A) 2 (B) 2, 3 (C) 6 3. (A) 2 (B) - 5, - 4 (C) 20 4. (A) 1 (B) 10 (C) 30 5. (A) 6 (B) None (C) 15 6. (A) 8 (B) None (C) 10 7. (A) 5 (B) 0, - 6 (C) 0 8. (A) 4 (B) - 7, 5 (C) 1,225 9. (A) 11 (B) - 5, - 2, 5 (C) - 12,800 10. (A) 10 (B) - 3, 5 2 , 3 (C) 164,025 11. (A) 4 (B) Negative 12. (A) 2 (B) Negative 13. (A) 5 (B) Negative 14. (A) 3 (B) Negative 15. (A) 1 (B) Negative 16. (A) 4 (B) Positive 17. (A) 6 (B) Positive 18. (A) 6 (B) Positive 19. 10 20. 7 21. 1 22. 0 23. (A) x int.: - 2; y int.: - 1 (B) Domain: all real numbers except 2 (C) Vertical asymptote: x = 2; horizontal asymptote: y = 1 (D) f ( x ) x 10 10 24. (A) x int.: 3; y int.: - 1 (B) Domain: all real numbers except - 3 (C) Vertical asymptote: x = - 3; horizontal asymptote: y = 1 (D) f ( x ) 10 10 x 25. (A) x int.: 0; y int.: 0 (B) Domain: all real numbers except - 2 (C) Vertical asymptote: x = - 2; horizontal asymptote: y = 3 (D) f ( x ) x 10 10 26. (A) x int.: 0; y int.: 0 (B) Domain: all real numbers except 3 (C) Vertical asymptote: x = 3; horizontal asymptote: y = 2 (D) f ( x ) 10 10 x 27. (A) x int.: 2; y int.: - 1 (B) Domain: all real numbers except 4 (C) Vertical asymptote: x = 4; horizontal asymptote: y = - 2 (D) f ( x ) x 10 10 28. (A) x int.: 1; y int.: - 3 2 (B) Domain: all real numbers except 2 (C) Vertical asymptote: x = 2; horizontal asymptote: y = - 3 (D) f ( x ) 10 10 x 29. (A) (B) 30. (A) (B) 31. (A) (B) 32. (A) (B) 33. y = 5 6 34. y = 3 2 35. y = 1 4 36. y = - 1 2 37. y = 0 38. y = 0 39. None 40. None 41. x = - 1 , x = 1 , x = - 3 , x = 3 42. x = - 2, x = 2, x = - 4, x = 4 43. x = 5 44. x = - 8 45. x = - 6 , x = 6 46. x = 0, x = 2 47. (A) x int.: 0; y int.: 0 (B) Vertical asymptotes: x = - 2 , x = 3 ; horizontal asymptote: y = 2 (C) f ( x ) x 10 10 (D) 48. (A) x int.: 0; y int.: 0 (B) Vertical asymptotes: x = - 3, x = 2 ; horizontal asymptote: y = 3 (C) f ( x ) 8 10 x (D) 49. (A) x int.: { 1 3 ; y int.: - 2 3 (B) Vertical asymptotes: x = - 3 , x = 3 ; horizontal asymptote: y = - 2 (C) f ( x ) x 10 10

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    A-10 Answers (D) 10 2 10 10 2 10 50. (A) x int.: { 1; y int.: - 3 4 (B) Vertical asymptote: x = - 2, x = 2; horizontal asymptote: y = - 3 (C) f ( x ) 10 10 x (D) 10 2 10 10 2 10 51. (A) x int.: 6; y int.: - 4 (B) Vertical asymptotes: x = - 3, x = 2; horizontal asymptote: y = 0 (C) f ( x ) x 10 10 (D) 10 2 10 10 2 10 52. (A) x int.: 2; y int.: 5 6 (B) Vertical asymptotes: x = - 4, x = 3; horizontal asymptote: y = 0 (C) f ( x ) 10 10 x (D) 10 2 10 10 2 10 53. f 1 x 2 = x 2 - x - 2 54. f 1 x 2 = 2 - x - x 2 55. f 1 x 2 = 4 x - x 3 56. f 1 x 2 = x 3 - x 57. (A) C 1 x 2 = 180 x + 200 (B) C 1 x 2 = 180 x + 200 x 58. (A) C 1 x 2 = 240 x + 300 (B) C 1 x 2 = 240 x + 300 x (C) C ( x ) x 600 30 (D) $240 per board 59. (A) C 1 n 2 = 2,500 + 175 n + 25 n 2 n (B) n 1,50 0 20 0 C ( n ) (C) 10 yr; $675.00 per year (D) 10 yr; $675.00 per year 60. (A) C 1 x 2 = x 2 + 2 x + 2,000 x (B) x 150 C ( x ) 500 (C) 45 units; $91.44 per player (D) 45 units; $91.44 per player 61. (A) C 1 x 2 = 0.00048 1 x - 500 2 3 + 60,000 x (B) (C) 750 cases per month; $90 per case 62. (A) C 1 x 2 = 20 x 3 - 360 x 2 + 2,300 x - 1,000 x (B) (C) 8.667 thousand cases per month; $567 per case 63. (A) (B) 1.7 lb 64. (A) (B) 583 eggs 65. (A) 0.06 cm/sec (B) v ( x ) x 5 100 66. (A) 55 words per minute (B) x 30 f ( x ) 60 67. (A) (B) 5.5 68. (A) (B) 2.5 (C) x 500 30 0 C ( x ) (D) $180 per board

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    Answers A-11 Exercises 2.5 1. (A) k (B) g (C) h (D) f 2. (A) g (B) f (C) h (D) k 3. y x 30 4 2 4 4. y 30 4 x 5. y x 30 4 2 4 6. y 30 4 x 7. f ( x ) x 2 30 4 2 4 8. g 2 30 4 x 9. y x 2 20 4 2 4 10. y 2 20 4 x 11. The graph of g is the graph of f reflected in the x axis. 12. The graph of g is the graph of f shifted 2 units to the right. 13. The graph of g is the graph of f shifted 1 unit to the left. 14. The graph of g is the graph of f reflected in the x axis. 15. The graph of g is the graph of f shifted 1 unit up. 16. The graph of g is the graph of f shifted 2 units down. 17. The graph of g is the graph of f vertically stretched by a factor of 2 and shifted to the left 2 units. 18. The graph of g is the graph of f vertically shrunk by a factor of 0.5 and shifted 1 unit to the right. 19. (A) y x 5 5 (B) y x 5 5 (C) y x 5 5 (D) y x 5 4 20. (A) y x 5 5 (B) y x 5 5 (C) y x 5 5 (D) y x 5 5 21. f ( t ) t 10 30 2 30 22. G ( t ) 10 250 t 23. y x 20 2 10 5 2 5 24. y 20 5 x 25. y x 20 4 2 4 26. y 1 4 x 27. a = 1 , - 1 28. a = 2, b = - 2, for example 29. x = 48 30. x = 9 31. x = - 2 , 5 32. x = - 6, 7 33. x = - 9 34. x = 16 35. x = 3 , 19 36. x = 0, 2 37. x = - 4, - 3 38. x = 1, 11 39. x = - 7 40. x = 1 > 2 41. x = - 2, 2 42. x = - 3, 3 43. x = 1 > 4 44. No solution 45. No solution 46. x = 2 > 3 47. h ( x ) x 2 0.5 2 5 48. y x 0.5 4 49. N t 10 0 5 50. N t 20 0 5 51. $16,064.07 52. $32,542.72 53. (A) $2,633.56 (B) $7,079.54 54. (A) $4,121.75 (B) $7,285.95 55. $10,706 56. $15,705 57. (A) $10,095.41 (B) $10,080.32 (C) $10,085.27 58. (A) $10,697.09 (B) $10,671.21 (C) $10,644.93 59. N approaches 2 as t increases without bound. N t 2 50 60. 40 boards per day N t 40 30 62. (A) 61. (A) (B) 9.94 billion (B) 268.8 exabytes per month 63. (A) 10% (B) 1% 64. (A) 62% (B) 39% 65. (A) P = 12 e 0.0402 x (B) 17.9 million 66. (A) P = 204 e 0.0077 x (B) 229 million 67. (A) P = 127 e - 0.0016 x (B) 124 million 68. (A) P = 7.4 e 0.0113 x (B) 2025: 8.2 billion; 2033: 9.0 billion Exercises 2.6 1. 27 = 3 3 2. 32 = 2 5 3. 10 0 = 1 4. e 0 = 1 5. 8 = 4 3 > 2 6. 27 = 9 3 > 2 7. log 7 49 = 2 8. log 6 36 = 2 9. l og 4 8 = 3 2 10. log 27 9 = 2 > 3 11. log b A = u 12. log b M = x 13. 6 14. - 3 15. - 5 16. 4 17. 7 18. - 6 19. - 3 20. Not defined 21. Not defined 22. - 1 23. log b P - log b Q 24. log b F + log b G 25. 5 log b L 26. 15 log b w 27. q p 28. log R P 29. x = 1 > 10 30. x = 10 31. b = 4 32. b = 1 > 5 33. y = - 3 34. y = 1 > 2 35. b = 1 > 3 36. b = 100 37. x = 8 38. x = 32 39. False 40. False 41. True 53. No solution 54. x = 4 55. y x 5 10 56. y 5 8 x 57. The graph of y = log 2 1 x - 2 2 is the graph of y = log 2 x shifted to the right 2 units. 59. Domain: 1 - 1, ∞ 2 ; range: all real numbers 60. Domain: 1 1, ∞ 2 ; range: all real numbers 61. (A) 3.547 43 (B) - 2.160 32 (C) 5.626 29 (D) - 3.197 04 62. (A) 1.860 96 (B) - 1.480 95 (C) 10.603 04 (D) - 5.128 36 63. (A) 13.4431 (B) 0.0089 (C) 16.0595 (D) 0.1514 64. (A) 121.1156 (B) 0.0089 (C) 22.9565 (D) 0.0132 65. 1.0792 66. 2.1847 67. 1.4595 68. - 1.1845 69. 18.3559 70. 8.7507 71. Increasing: 1 0, ∞ 2 y x 3 5 72. Decreasing: 1 0, ∞ 2 y 3 x 5 42. False 43. True 44. False 45. False 46. True 47. x = 2 48. x = 12 49. x = 8 50. x = 2 51. x = 7 52. x = 4

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    A-12 Answers 73. Decreasing: 1 0, 1 4 Increasing: 3 1, ∞ 2 y x 5 5 74. Decreasing: 1 - ∞ , 0 2 Increasing: 1 0, ∞ 2 y 3 5 x 75. Increasing: 1 - 2, ∞ 2 y x 5 5 76. Increasing: 1 0, ∞ 2 y 6 x 5 77. Increasing: 1 0, ∞ 2 y 10 10 x 78. Increasing: 1 3, ∞ 2 y 10 x 10 79. Because b 0 = 1 for any permissible base b 1 b 7 0, b  1 2 . 80. Because the function y = 1 x is not one-to-one 81. x 7 1 x 7 ln x for 1 6 x … 16 82. log x 6 1 3 x 6 x 83. 4 yr 84. 8 yr 85. 9.87 yr; 9.80 yr 86. 5.17 yr; 5.09 yr 87. 7.51 yr 88. 29.84 yr 89. (A) 5,373 90. Equilibrium price: $46.77; Equilibrium quantity: 6,145 92. (A) 30 (B) 65 (C) 80 (D) 150 93. 168 bushels/acre (B) 7,220 94. 12,628 million bushels 95. 912 yr 96. 18,569 yr 21. (A) x intercepts: - 4, 0 ; y intercept: 0 (B) Vertex: 1 - 2, - 4 2 (C) Min- imum: - 4 (D) Range: y Ú - 4 or 3 - 4, ∞ 2 (2.3) 22. Quadratic (2.3) 23. Linear (2.1) 24. None (2.1, 2.3) 25. Constant (2.1) 26. x = 8 (2.6) 27. x = 3 (2.6) 28. x = 3 (2.5) 29. x = - 1, 3 (2.5) 30. x = 0, 3 2 (2.5) 31. x = - 2 (2.6) 32. x = 1 2 (2.6) 33. x = 27 (2.6) 34. x = 13.3113 (2.6) 35. x = 158.7552 (2.6) 36. x = 0.0097 (2.6) 37. x = 1.4359 (2.6) 38. x = 1.4650 (2.6) 39. x = 92.1034 (2.6) 40. x = 9.0065 (2.6) 41. x = 2.1081 (2.6) 42. (A) All real numbers except x = - 2 and 3 (B) x 6 5 (2.1) 43. Vertex form: 4 a x + 1 2 b 2 - 4 ; x intercepts: - 3 2 and 1 2 ; y intercept: - 3 ; vertex: 1 - 1 2 , - 4 2 ; minimum: - 4 ; range: y Ú - 4 or 3 - 4, ∞ 2 (2.3) 44. 1 - 1.54, - 0.79 2 ; 1 0.69, 0.99 2 (2.5, 2.6) 45. y x 50 5 (2.1) 46. y x 10 5 (2.1) 47. 6 (2.1) 48. - 19 (2.1) 49. 10 x - 4 (2.1) 50. 21 - 5 x (2.1) 51. (A) - 1 (B) - 1 - 2 h (C) - 2 h (D) - 2 (2.1) 52. (A) a 2 - 3 a + 1 (B) a 2 + 2 ah + h 2 - 3 a - 3 h + 1 (C) 2 ah + h 2 - 3 h (D) 2 a + h - 3 (2.1) 53. The graph of function m is the graph of y =  x  reflected in the x axis and shifted to the right 4 units. (2.2) 54. The graph of function g is the graph of y = x 3 vertically contracted by a factor of 0.3 and shifted up 3 units. (2.2) 55. The graph of y = x 2 is vertically expanded by a factor of 2, reflected in the x axis, and shifted to the left 3 units. Equation: y = - 2 1 x + 3 2 2 . (2.2) 56. f 1 x 2 = 2 2 x + 3 - 1 (2.2) x 5 5 f ( x ) 57. y = 0 (2.4) 58. y = 3 4 (2.4) 59. None (2.4) 60. x = - 10, x = 10 (2.4) 61. x = - 2 (2.4) 62. True (2.3) 63. False (2.3) 64. False (2.3) 65. True (2.4) 66. True (2.5) 67. True (2.3) 68. y x 15 40 (2.2) 69. y x 80 50 (2.2) Chapter 2 Review Exercises 1. y x 10 5 (2.1) 2. y x 5 5 (2.1) 3. x 5 5 y (2.1) 4. (A) Not a function (B) A function (C) A function (D) Not a function (2.1) 5. (A) - 2 (B) - 8 (C) 0 (D) Not defined (2.1) 6. v = ln u (2.6) 7. y = log x (2.6) 8. M = e N (2.6) 9. u = 10 v (2.6) 10. x = 9 (2.6) 11. x = 6 (2.6) 12. x = 4 (2.6) 13. x = 2.157 (2.6) 14. x = 13.128 (2.6) 15. x = 1,273.503 (2.6) 16. x = 0.318 (2.6) 17. (A) y = 4 (B) x = 0 (C) y = 1 (D) x = - 1 or 1 (E) y = - 2 (F) x = - 5 or 5 (2.1) 18. (A) x 5 5 y (B) x 5 5 y (C) x 5 5 y (D) x 5 5 y (2.2) 19. f 1 x 2 = - 1 x - 2 2 2 + 4 . The graph of f 1 x 2 is the graph of y = x 2 reflected in the x axis, then shifted right 2 units and up 4 units. (2.2) 20. (A) g (B) m (C) n (D) f (2.2, 2.3) 70. y = - 1 x - 4 2 2 + 3 (2.2, 2.3) 71. f 1 x 2 = - 0.4 1 x - 4 2 2 + 7.6 (A) x intercepts: - 0.4, 8.4 ; y intercept: 1.2 (B) Vertex: 1 4.0, 7.6 2 (C) Maximum: 7.6 (D) Range: y … 7.6 or 1 - ∞ , 7.6 4 (2.3) 72. (A) x intercepts: - .4, 8.4 ; y inter- cept: 1.2 (B) Vertex: (4.0, 7.6) (C) Maximum: 7.6 (D) Range: y … 7.6 or 1 - ∞ , 7.6] (2.3) 73. log 10 p = p and 10 log 1 2 = 1 2; ln e p = p and e ln 1 2 = 1 2 (2.6) 74. x = 2 (2.6) 75. x = 2 (2.6) 76. x = 1 (2.6) 77. x = 300 (2.6) 78. y = ce - 5 t (2.6) 79. If log 1 x = y , then 1 y = x ; that is, 1 = x for all positive real numbers x , which is not possible. (2.6) 80. The graph of y = 2 3 x is vertically expanded by a factor of 2, reflected in the x axis, and shifted 1 unit left and 1 unit down. Equation: y = - 2 2 3 x + 1 - 1. (2.2) 81. G 1 x 2 = 0.3 1 x + 2 2 2 - 8.1 (A) x intercepts: - 7.2, 3.2 ; y intercept: - 6.9 (B) Vertex: 1 - 2, - 8.1 2 (C) Minimum: - 8.1 (D) Range: y Ú - 8.1 or 3 - 8.1, ∞ 2 (2.3)

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    Answers A-13 82. (A) x intercepts: - 7.2. 3.2; y intercept: - 6.9 (B) Vertex: 1 - 2, - 8.1 2 (C) Minimum: - 8.1 (D) Range: y Ú - 8.1 or [ - 8.1, ∞ 2 (2.3) 83. (A) S 1 x 2 = μ 3 if 0 … x … 20 0.057 x + 1.86 if 20 6 x … 200 0.0346 x + 6.34 if 200 6 x … 1,000 0.0217 x + 19.24 if x 7 1,000 (B) S ( x ) x 50 1,500 (2.2) 84. $5,321.95 (2.5) 85. $5,269.51 (2.5) 86. 201 months 1 ≈ 16.7 years 2 (2.5) 87. 9.38 yr (2.5) 88. (A) R ( x ) C ( x ) x 600 40 C R (B) R = C for x = 4.686 thou- sand units (4,686 units) and for x = 27.314 thousand units (27,314 units); R 6 C for 1 … x 6 4.686 or 27.314 6 x … 40; R 7 C for 4.686 6 x 6 27.314. (C) Maxi- mum revenue is 500 thousand dollars ($500,000). This occurs at an output of 20 thousand units (20,000 units). At this output, the wholesale price is p 1 20 2 = $25. (2.3) 89. (A) P 1 x 2 = R 1 x 2 - C 1 x 2 = x 1 50 - 1.25 x 2 - 1 160 + 10 x 2 (B) P = 0 for x = 4.686 thou- sand units (4,686 units) and for x = 27.314 thousand units (27,314 units); P 6 0 for 1 … x 6 4.686 or 27.314 6 x … 40; p 7 0 for 4.686 6 x 6 27.314. (C) Maximum profit is 160 thousand dollars ($160,000). This occurs at an output of 16 thousand units (16,000 units). At this output, the wholesale price is p 1 16 2 = $30. (2.3) 90. (A) A 1 x 2 = - 3 2 x 2 + 420 x (B) Domain: 0 … x … 280 (C) A ( x ) x 30,0 00 300 (D) There are two solutions to the equation A 1 x 2 = 25,000, one near 90 and another near 190. (E) 86 ft; 194 ft (F) Maximum combined area is 29,400 ft 2 . This occurs for x = 140 ft and y = 105 ft. (2.3) 91. (A) 2,833 sets (B) 4,836 (C) Equilibrium price: $131.59; equi- librium quantity: 3,587 cookware sets (2.3) 92. (A) (B) 4976 (2.4) 93. (A) N = 2 2 t or N = 4 t (B) 15 days (2.5) 94. k = 0.009 42; 489 ft (2.6) 95. (A) 6,134,000 (2.6) 96. 23.1 yr (2.5) 97. (A) $1,319 billion (B) 2031 (2.5)

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    Chapter 3 Exercises 3.1 1. $25.42 2. $1,461.32 3. 64% 4. 4 5. Slope = 120 ; y int. = 12,000 6. Slope = 300 ; y int. = 15,000 7. Slope = 50 ; y int. = 2,000 8. Slope = 175 ; y int. = 5,000 9. 0.062 10. 8.5% 11. 13.7% 12. 0.0435 13. 0.0025 14. 0.19% 15. 0.84% 16. 0.0036 17. 1 2 yr 18. 3 4 yr 19. 1 3 yr 20. 1 4 yr 21. 5 4 yr 22. 3 26 yr 23. 10 13 yr 24. 7 4 yr 25. $42 26. $85.50 27. $1,800 28. $250 29. 0.12 or 12% 30. 0.16 or 16% 31. 1 2 yr 32. 3 4 yr 33. $4,612.50 34. $3,011.25 35. $875 36. $5,600 37. 0.36 or 36% 38. 0.22 or 22% 39. 1 yr 40. 1 4 yr 41. r = I > 1 Pt 2 42. P = I rt 43. P = A > 1 1 + rt 2 44. r = A - P Pt 45. t = A - P Pr 46. t = I Pr 47. The graphs are linear, all with y intercept $1,000; their slopes are 40, 80, and 120, respectively. 48. The graphs are linear, with y intercepts 400, 800, and 1,200 and slopes 30, 60, and 90, respectively. 49. $45 50. $232.50 51. $30 52. $41.67 53. $7,647.20 54. $10,325.00 55. 8.1% 56. 7.8% 57. 18% 58. 24% 59. $1,604.40; 20.88% 60. $3,106.20; 21.24% 61. 4.298% 62. 4.205% 63. $992.38 64. $976.07 65. $24.31 66. $20.00 67. $27 68. $27.82 69. 5.396% 70. 6.697% 71. 6.986% 72. 22.112% 73. 12.085% 74. 6.352% 75. 109.895% 76. 53.454% 77. 87.158% 78. 42.72% 79. $118.94 80. $22.41 81. $1,445.89 82. $1,953.60 83. $7.27 84. $17.59 85. $824.85 86. $648.10 87. 630% 88. 429% 89. 771% 90. 431% Exercises 3.2 1. P = 950 2. P = 2,500 3. x = 17 4. x = 3.5 5. i = 0.5 6. i = 0.4 7. n = 4 8. n = 5 9. $5,983.40 10. $3,008.71 11. $4,245.07 12. $11,352.53 13. $3,125.79 14. $1,544.94 15. $2,958.11 16. $12,935.03 17. 2.5 yr 18. 3.25 yr 19. 6.79% 20. 4.18% 21. 1.65% 22. 0.32% 23. 0.46% 24. 1.47% 25. 0.02% 26. 1.36% 27. 2.43% 28. 0.03% 29. 3.46% 30. 6.28% 31. 6.36% 32. 4.38% 33. 8.76% 34. 7.38% 35. 2.92% 36. 5.64% 37. (A) $126.25; $26.25 (B) $126.90; $26.90 (C) $127.05; $27.05 38. (A) $2,805.10; $805.10 (B) $2,829.56; $829.56 (C) $2,835.25; $835.25 39. (A) $5,524.71 (B) $6,104.48 40. (A) $24,419.93 (B) $27,527.90 41. $12,175.69 42. $174,250.55 43. All three graphs are increasing, curve upward, and have the same y intercept; the greater the interest rate, the greater the increase. The amounts at the end of 8 years are $1,376.40, $1,892.46, and $2,599.27, respectively. 44. All three graphs are increasing and curve upward; they have y intercepts 4,000, 8,000 and 12,000, respectively. The amounts at the end of 8 years are $7,274.88, $14,549.76, and $21,824.64, respectively. 45. Period Interest Amount 0 $1,000.00 1 $97.50 $1,097.50 2 $107.01 $1,204.51 3 $117.44 $1,321.95 4 $128.89 $1,450.84 5 $141.46 $1,592.29 6 $155.25 $1,747.54 46. Period Interest Amount 0 $2,000.00 1 $165.00 $2,165.00 2 $178.61 $2,343.61 3 $193.35 $2,536.96 4 $209.30 $2,746.26 5 $226.57 $2,972.83 47. (A) $7,440.94 (B) $5,536.76 48. (A) $4,730.96 (B) $3,730.33 49. (A) $19,084.49 (B) $11,121.45 50. (A) $2,970.16 (B) $2,072.21 51. (A) 3.97% (B) 2.32% 52. (A) 4.41% (B) 4.40% 53. (A) 5.28% (B) 5.27% 54. (A) 3.09% (B) 2.99% 55. 1 1 2 3 yr 56. 5.75 yr 57. 3.75 yr 58. 8.5 yr 59. n ≈ 12 60. n ≈ 15 61. (A) 7 1 4 yr (B) 6 yr 62. (A) 9 yr (B) 10.5 yr 63. (A) 7.7 yr (B) 6.3 yr 64. (A) 3.3 yr (B) 2.1 yr 65. $65,068.44 66. $16,961.66 67. $282,222.44 68. $20,683.10 69. $19.78 per ft 2 per mo 70. $173,391.50 71. (A) In 2026, 250 years after the signing, it would be worth $175,814.55. (B) If interest were compounded monthly, daily, or continuously, it would be worth $179,119.92, $180,748.53, or $180,804.24, respectively. (C) 73. 9.66% 74. 5.58% 75. 2 yr, 10 mo 76. 17 quarters or 4.25 yr 77. $163,295.21 78. $180,370,243.40; $20.20 79. 3,615 days; 8.453 yr 80. 8,021 days; 18.310 yr 81. Years Exact Rate Rule of 72 6 12.2 12.0 7 10.4 10.3 8 9.1 9.0 9 8.0 8.0 10 7.2 7.2 11 6.5 6.5 12 5.9 6.0 82. 83. 14 quarters 84. 17 months 85. To maximize earnings, choose 10% simple interest for investments lasting fewer than 11 years and 7% compound interest otherwise. 86. To maximize earnings, choose 9% simple interest for investments lasting fewer than 154 months and 6% compounded monthly otherwise. 87. 3.33% 88. 2.91% 89. 7.02% 90. 5.99% 91. $15,843.80 92. $13,261.81 93. 4.53% 94. 4.56% 95. 13.44% 96. 17.61% 97. 17.62% 98. 20.30% Exercises 3.3 1. 1,023 2. 488,281 3. 3,000 4. 25 5. 71,744,530 6. 444,444 7. i = 0.02 ; n = 80 8. i = 0.005 ; n = 72 9. i = 0.0375 ; n = 24 10. i = 0.0625 ; n = 15 11. i = 0.0075 ; n = 48 12. i = 0.0425 ; n = 14 13. i = 0.0595 ; n = 12 14. i = 0.019 ; n = 72 15. FV = $13,435.19 16. FV = $4,164.59 17. PMT = $310.62 18. PMT = $172.57 19. n = 17 20. n = 13 21. i = 0.09 22. i = 0.07 ANSWERS A-14

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    Answers A-15 25. n = ln a 1 + i FV PMT b ln 1 1 + i 2 26. i = FV PMT - 2 27. Value: $84,895.40; interest: $24,895.40 28. Value = $323,943.07 ; interest = $143,943.07 29. $20,931.01 30. $343,214.73 31. $667.43 32. $626.93 33. $763.39 34. $2,363.07 35. Period Amount Interest Balance 1 $1,000.00 $0.00 $1,000.00 2 $1,000.00 $83.20 $2,083.20 3 $1,000.00 $173.32 $3,256.52 4 $1,000.00 $270.94 $4,527.46 5 $1,000.00 $376.69 $5,904.15 36. Period Amount Interest Balance 1 $2,000.00 $0.00 $2,000.00 2 $2,000.00 $39.50 $4,039.50 3 $2,000.00 $79.78 $6,119.28 4 $2,000.00 $120.86 $8,240.14 5 $2,000.00 $162.74 $10,402.88 6 $2,000.00 $205.46 $12,608.34 7 $2,000.00 $249.01 $14,857.35 8 $2,000.00 $293.43 $17,150.78 37. First year: $33.56; second year: $109.64; third year: $190.41 38. First year: $60.80; second year: $109.64; third year: $190.41 39. $111,050.77 40. $84,852.51 41. $1,308.75 42. $2,308.75 43. (A) 1.540% (B) $202.12 44. (A) 2.220% (B) $9,528.64 45. 33 months 46. 45 months 47. 7.77% 48. 6.14% 49. 0.75% 50. 0.84% 51. After 11 quarterly 52. After 66 monthly payments Exercises 3.4 1. 511/256 2. 97,656/78,125 3. 33,333,333/1,000,000 4. 111,111,111/1,000,000 5. 171/256 6. 90,909/100,000 7. i = 0.006 ; n = 48 8. i = 0.0495 ; n = 24 9. i = 0.02475 ; n = 40 10. i = 0.0475 ; n = 5 11. i = 0.02525 ; n = 32 12. i = 0.0206 ; n = 24 13. i = 0.0548 ; n = 9 14. i = 0.009 ; n = 36 15. PV = $3,458.41 16. PV = $13,133.87 17. PMT = $586.01 18. PMT = $232.02 19. n = 29 20. n = 70 21. i = 0.029 22. i = 0.015 24. n = - ln a 1 - i PV PMT b ln 1 1 + i 2 27. $35,693.18 28. $55,135.98 29. $11,241.81; $1,358.19 30. $10,872.23; $1,727.77 31. $69.58; $839.84 32. $94.69; $2,181.40 33. 31 months 34. 36 months 35. 71 months 36. 57 months 37. For 0% financing, the monthly payments should be $242.85, not $299. If a loan of $17,485 is amortized in 72 payments of $299, the rate is 7.11% compounded monthly. 38. For 0% financing, the monthly payments should be $333.29, not $399. If a loan of $23,997 is amortized in 72 payments of $399, the rate is 6.11% compounded monthly. 39. The monthly payments with 0% financing are $455. If you take the rebate, the monthly payments are $434.24. You should choose the rebate. 40. The monthly payments with 0% financing are $475. If you take the rebate, the monthly payments are $437.08. You should choose the rebate. 41. $314.72; $17,319.68 42. $1,167.57; $26,075.88 43. Payment Number Payment Interest Unpaid Balance Reduction Unpaid Balance 0 $5,000.00 1 $706.29 $140.00 $566.29 4,433.71 2 706.29 124.14 582.15 3,851.56 3 706.29 107.84 598.45 3,253.11 4 706.29 91.09 615.20 2,637.91 5 706.29 73.86 632.43 2,005.48 6 706.29 56.15 650.14 1,355.34 7 706.29 37.95 668.34 687.00 8 706.24 19.24 687.00 0.00 Totals $5,650.27 $650.27 $5,000.00 44. Payment Number Payment Interest Unpaid Balance Reduction Unpaid Balance 0 $10,000.00 1 $1,821.58 $260.00 $1,561.58 8,438.42 2 1,821.58 219.40 1,602.18 6,836.24 3 1,821.58 177.74 1,643.84 5,192.40 4 1,821.58 135.00 1,686.58 3,505.82 5 1,821.58 91.15 1,730.43 1,775.39 6 1,821.55 46.16 1,775.39 0.00 Totals $10,929.45 $929.45 $10,000.00 45. First year: $466.05; second year: $294.93; third year: $107.82 46. $3,319.03 47. $97,929.78; $116,070.22 48. $671.25; $145,650 49. $143.85/mo; $904.80 50. $42,033.08 51. Monthly payment: $908.99 (A) $125,862 (B) $81,507 (C) $46,905 52. (A) $180,443 (B) $139,061 (C) $81,122 53. (A) Monthly payment: $1,015.68; interest: $114,763 (B) 197 months; interest saved: $23,499 54. (A) $2,469.03 (B) 90 55. (A) 157 (B) 243 (C) The withdrawals continue forever. 56. $522,241.29; $569,216.34; $668,430.68 57. (A) Monthly withdrawals: $1,229.66; total interest: $185,338.80 (B) Monthly deposits: $162.65 58. $664.99; $240,301.80 59. $65,584 60. $68,299 61. $34,692 62. $40,227.60 63. All three graphs are decreasing, curve downward, and have the same x intercept; the unpaid balances are always in the ratio 2:3:4. The monthly payments are $402.31, $603.47, and $804.62, with total interest amounting to $94,831.60, $142,249.20, and $189,663.20, respectively. 64. All three graphs are decreasing, curve downward, and have the same x and y intercepts; the greater the interest rate, the greater the unpaid balance. The monthly payments are $399.18,$526.54, and $663.72, with total interest amounting to $83,704.80, $129, 554.49, and $178,939.20, respectively. 65. 14.45% 66. 18.16% 67. 10.21% 68. 8.76% Chapter 3 Review Exercises 1. A = $104.50 (3.1) 2. P = $800 (3.1) 3. t = 0.75 yr , or 9 mo (3.1) 4. r = 6 % (3.1) 5. A = $1,393.68 (3.2) 6. P = $3,193.50 (3.2) 7. A = $5,824.92 (3.2) 8. P = $22,612.86 (3.2) 9. FV = $69,770.03 (3.3) 10. PMT = $115.00 (3.3) 11. PV = $33,944.27 (3.4) 12. PMT = $166.07 (3.4) 13. n ≈ 16 (3.2) 14. n ≈ 41 (3.3) 15. $3,350.00; $350.00 (3.1) 16. $19,654 (3.2) 17. $12,944.67 (3.2) 18. (A) Period Interest Amount 0 $400.00 1 $21.60 $421.60 2 $22.77 $444.37 3 $24.00 $468.36 4 $25.29 $493.65 (3.2)

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    A-16 Answers 19. To maximize earnings, choose 13% simple interest for investments lasting less than 9 years and 9% compound interest for investments lasting 9 years or more. (3.2) 20. $164,402 (3.2) 21. 7.83% (3.2) 22. 9% compounded quarterly, since its effective rate is 9.31%, while the effective rate of 9.25% compounded annually is 9.25% (3.2) 23. $25,861.65; $6,661.65 (3.3) 24. 288% (3.1) 25. $1,725.56 (3.1) 26. $29,354 (3.2) 27. $18,021 (3.2) 28. 15% (3.1) 29. The monthly payments with 0% financing are $450. If you take the rebate, the monthly payments are $426.66. You should choose the rebate. (3.4) 30. (A) 6.43% (B) 6.45% (3.2) 31. 9 quarters or 2 yr, 3 mo (3.2) 32. 139 mo; 93 mo (3.2) 33. (A) $571,499 (B) $1,973,277 (3.3) 34. 10.45% (3.2) 35. (A) 174% (B) 65.71% (3.1) 36. $725.89 (3.3) 37. (A) $140,945.57 (B) $789.65 (C) $136,828 (3.3, 3.4) 38. $102.99; $943.52 (3.4) 39. $576.48 (3.3) 40. 3,374 days; 10 yr (3.2) 41. $175.28; $2,516.80 (3.4) 42. $13,418.78 (3.2) 43. 5 yr, 10 mo (3.3) 44. 18 yr (3.4) 45. 28.8% (3.1) (B) Period Interest Payment Balance 1 $100.00 $100.00 2 $5.40 $100.00 $205.40 3 $11.09 $100.00 $316.49 4 $17.09 $100.00 $433.58 (3.3) Payment Number Payment Interest Unpaid Balance Reduction Unpaid Balance 0 $1,000.00 1 $265.82 $25.00 $240.82 759.18 2 265.82 18.98 246.84 512.34 3 265.82 12.81 253.01 259.33 4 265.81 6.48 259.33 0.00 Totals $1,063.27 $63.27 $1,000.00 47. 28 months (3.3) 48. $55,347.48; $185,830.24 (3.3) 49. 2.47% (3.2) 50. 6.33% (3.1) 51. 44 deposits (3.3) 52. (A) $1,189.52 (B) $72,963.07 (C) $7,237.31 (3.4) 53. The certificate would be worth $53,394.30 when the 360th payment is made. By reducing the principal, the loan would be paid off in 252 months. If the monthly payment were then invested at 7% compounded monthly, it would be worth $67,234.20 at the time of the 360th payment. (3.2, 3.3, 3.4) 54. The lower rate would save $12,247.20 in interest payments. (3.4) 55. $3,807.59 (3.2) 56. 5.79% (3.2) 57. $4,844.96 (3.1) 58. $6,697.11 (3.4) 59. 7.24% (3.2) 60. (A) $398,807 (B) $374,204 (3.3) 61. $15,577.64 (3.2) 62. (A) 30 yr: $569.26; 15 yr: $749.82 (B) 30 yr: $69,707.99; 15 yr: $37,260.74 (3.4) 63. $20,516 (3.4) 64. 33.52% (3.4) 65. (A) 10.74% (B) 15 yr: 40 yr (3.3) 46.

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