Skip to content
Textbook Guides

Solution Manual for Calculus and Its Applications, 2nd Edition

Solution Manual for Calculus and Its Applications, 2nd Edition simplifies even the toughest textbook questions with step-by-step solutions and easy explanations.

Preview 16 of 99 pages

See the first 16 pages exactly as they appear in the document.

  1. Page 1
    Read page 1 as text

    A-1 ANSWERS: CHAPTER R Technology Connection, p. 7 1. Left to the student Exercise Set R.1, p. 10 1. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = x − 1 2. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = x + 4 3. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = − x 1 4 4. y x –1 –2 1 2 2 3 4 1 –1 –2 –3 –4 –3 –4 –5 3 4 5 5 –5 y = –3 x 5. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = − x + 3 5 3 6. y x –1 –2 1 2 2 3 4 1 –1 –2 –3 – 4 –3 – 4 – 5 3 4 5 5 – 5 2 – 3 y = x – 4 7. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y x + y = 5 8. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y x − y = 4 9. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y 6 x + 3 y = −9 10. y x –1 –2 1 2 2 3 4 1 –1 –2 –3 – 4 –3 – 4 – 5 3 4 5 5 – 5 8 y – 2 x = 4 11. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y 2 x + 5 y = 10 12. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y 5 x − 6 y = 12 13. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = x 2 − 5 14. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = x 2 − 3 15. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y x = y 2 + 2 16. y x –1 –2 1 2 2 3 4 1 –1 –2 –3 – 4 –3 – 4 – 5 3 4 5 5 – 5 x = 2 – y 2 17. y = 5 y - 1 - 2 - 1 - 3 - 4 - 5 x 1 2 3 4 5 - 2 2 3 4 1 18. y = - 2 y - 1 - 2 - 1 - 3 - 4 - 5 x 1 2 3 4 5 - 3 2 3 4 1 19. 1 −1 −1 −2 −3 −2 −3 −4 −5 2 3 4 5 5 4 7 6 3 2 1 x y y = 7 − x 2 20. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = 5 − x 2 21. 1 −1 −1 −2 −3 −4 −5 2 3 4 5 5 4 3 2 9 8 7 6 1 x y y − 7 = x 3 22. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y + 1 = x 3 Answers

  2. Page 2
  3. Page 3
    Read page 3 as text

    A-2 A N S W E R S 29. (a) f 1 x 2 = 4 x + 2; (b) 1 −1 −1 2 3 4 5 5 4 7 6 3 2 1 x y f ( x ) = 4 x + 2 30. (a) g 1 x 2 = - 3 x - 4; (b) 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y g ( x ) = −3 x − 4 31. (a) h 1 x 2 = x 2 + x ; (b) 1 −1 −1 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y h ( x ) = x 2 + x 32. (a) k 1 x 2 = x 2 - 3 x ; (b) 1 −1 −1 −2 −3 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y k ( x ) = x 2 − 3 x 33. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y f ( x ) = 2 x − 5 34. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y f ( x ) = 3 x − 1 35. y x –1 –2 1 2 2 3 4 1 g ( x ) = –4 x –1 –2 –3 –4 36. g ( x ) = −2 x 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y 37. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y f ( x ) = x 2 − 2 38. 1 −1 −1 −2 −3 −4 −5 2 3 4 5 5 4 3 2 9 8 7 6 1 x y f ( x ) = x 2 + 4 23. 344.4 mg 24. 1954: 3.99 min, 2000: 3.71 min, 2025: 3.56 min 25. (a) 18.62°; (b) 32.92°; (c) 43.56° 26. (a) 35.5 mm; (b) 93.5 mm; (c) in 2022 27. (a) 3.50 million; (b) 2024 28. (a) 3.38 million; (b) 3.28 million; (c) answers may vary. 29. About 27.25 mi/hr 30. About 1.32 sec 31. (a) $102,800; (b) $102,819.60; (c) $102,829.54; (d) $102,839.46; (e) $102,839.56 32. (a) $306,600; (b) $306,636.30; (c) $306,654.65; (d) $306,672.93; (e) $306,673.13 33. (a) $33,745.92; (b) $33,784.87; (c) $33,804.75; (d) $33,824.68; (e) $33,824.90 34. (a) $1215.51; (b) $1218.40; (c) $1219.89; (d) $1221.39; (e) $1221.40 35. $536.25 36. $389.94 37. $70,561.01 38. $1635.99 39. (a) 2008–2014; (b) 2006–2008 and 2014–2016; (c) 2010, 9.6%; (d) 2006–2007, 4.6% 40. Answers may vary. 41. (a) $88,382.67; (b) $42,000, $46,382.67 42. (a) $653.76; (b) $117,676.80, $42,000, $75,676.80 43. 5.43% 44. 4.16% 45. 3.82% 46. 4.08% 47. (a) Western 2.5%, Commonwealth 2.46%; (b) Western’s account 48. (a) Sierra 3%, Foothill 3.01%; (b) Foothill’s account 49. 2.179% 50. 3.699% 51. – 10 –10 10 10 0 –2 –2 2 2 0 The window 3 - 2, 2, - 2, 2 4 shows better detail around the origin. 52. – 10 –10 10 10 0 The graph appears to touch the x -axis, but using a smaller window reveals that it does not actually do so. Technology Connection, p. 16 1. 951; 42,701 2. 21,813 Exercise Set R.2, p. 20 1. Yes 2. Yes 3. Yes 4. No 5. Yes 6. Yes 7. Yes 8. Yes 9. Yes 10. Yes 11. No 12. No 13. Yes 14. Yes 15. Yes 16. Yes 17. No 18. No 19. Yes 20. Yes 21. No 22. No 23. (a) 17.4, 17.04, 17.004, 17; (b) 13, 9, - 11, 4 k - 3, 4 x + 4 h - 3 24. (a) 14.3, 14.03, 14.003, 14; (b) 17, - 1, 3 k + 2, 3 x + 3 h + 2 25. - 2, - 3, - 2, 22, a 2 + 2 ah + h 2 - 3, 2 x + h , for h ? 0 26. 13, 4, 5, 53, a 2 + 2 ah + h 2 + 4, 2 x + h , for h ? 0 27. 1 49 , 1 9 , 1 1 a + 3 2 2 , 1 1 x + h + 3 2 2 , - 2 x - h - 6 1 x + h + 3 2 2 1 x + 3 2 2 28. 1 4 , 1 36 , 1 1 k - 5 2 2 , 1 1 x + h - 5 2 2

  4. Page 4
    Read page 4 as text

    A N S W E R S A-3 67. 1 −1 −1 −2 −3 −4 −5 2 3 4 5 5 4 3 2 9 8 7 6 1 x y y = f ( x ) 68. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = f ( x ) 69. 1 −1 −1 −2 −3 −2 −3 −4 −5 2 3 4 5 5 4 7 6 3 2 1 x y y = f ( x ) 70. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = g ( x ) 71. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = g ( x ) 72. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = g ( x ) 73. 1 −1 −1 −2 −3 −4 −5 −6 −7 −2 −3 −4 −5 2 3 4 5 3 2 1 x y y = f ( x ) 74. 1 −1 −1 −2 −3 −4 −5 −6 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = f ( x ) 75. $530.80 76. $875.05 77. (a) 1.818 m 2 ; (b) 2.173 m 2 ; (c) 1.537 m 2 78. (a) 1.708 m 2 ; (b) 1.871 m 2 79. (a) Yes; (b) yes; (c) no; (d) yes 80. (a) Yes, a unique number that rates the scale of impact is assigned to each event. (b) The inputs are the events, the outputs are the scale-of-impact numbers. 81. y = 5; yes 82. y = { A x + 5 2 ; no 83. y = { 2 x ; no 84. y = 2 2 3 x ; yes 85. Answers may vary. 86. 2, 0, - 2, 2 87. X X = −3 Y1 −10 −8 −14 20 142 400 842 −3 −1 1 3 5 7 9 88. X X = −3 Y1 .6 ERROR −1 −.75 −1 ERROR .6 −3 −2 −1 0 1 2 3 89. Left to the student 90. Left to the student 91. (a) f 1 x 2 = 5 1 x + 2 2 , g 1 x 2 = 5 x + 2; 39. 1 −1 −1 −2 −3 −2 −3 −4 −5 2 3 4 5 5 4 7 6 3 2 1 x y f ( x ) = 6 − x 2 40. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y g ( x ) = − x 2 + 1 41. y x 1 2 8 –8 4 –4 1 –1 –1 –2 g ( x ) = x 3 42. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y g ( x ) = x 3 1 2 43. Yes 44. Yes 45. No 46. Yes 47. Yes 48. No 49. Yes 50. No 51. Yes 52. Yes 53. Yes 54. Yes 55. No 56. No 57. (a) 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y x = y 2 − 2 (b) No, the graph fails the vertical-line test. 58. (a) 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y x = y 2 − 3 (b) No, the graph fails the vertical-line test. 59. 2 x + h - 3, for h ? 0 60. 2 x + h + 4, for h ? 0 61. 3, - 2 62. 7, 6 63. 17, 6 64. 11, 3.5 65. y x –1 –2 1 2 2 3 4 1 –1 –2 –3 –4 –3 –4 –5 3 4 5 5 –5 y = f ( x ) 66. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = f ( x )

  5. Page 5
    Read page 5 as text

    A- 4 A N S W E R S 36. 3 2, ` 2 [2, q ) 2 37. R ( -q , q ) 38. R ( -q , q ) 39. 1 - ` , 2 2 < 1 2, ` 2 ( -q , 2) ´ (2, q ) 2 40. 1 - ` , 2 2 < 1 2, ` 2 ( -q , 2) ´ (2, q ) 2 41. R ( -q , q ) 42. R ( -q , q ) 43. ¢ - ` , 7 2 ≤ < ¢ 7 2 , ` ≤ 7 2 q , ´ , q 7 2 7 2 - ( ) ( ) 44. ¢ - ` , 9 2 ≤ < ¢ 9 2 , ` ≤ 9 2 q , ´ , q 9 2 9 2 - ( ) ( ) 45. J - 4 5 , ` ≤ 4 5 - 4 5 - [ , q ) 46. ¢ - ` , 2 3 R 2 3 2 3 ( -q , ] 47. R ( -q , q ) 48. R ( -q , q ) 49. 1 - ` , - 5 2 < 1 - 5, 5 2 < 1 5, ` 2 ( -q , - 5) ´ ( - 5, 5) ´ (5, q ) - 5 5 50. 1 - ` , - 6 2 < 1 - 6, 6 2 < 1 6, ` 2 ( -q , - 6) ´ ( - 6, 6) ´ (6, q ) - 6 6 51. R ( -q , q ) 52. R ( -q , q ) 53. 3 - 1, 3 4 - 1 3 [ - 1, 3] 54. J - 3 2 , 12 5 R 3 2 - 3 2 12 5 12 5 3 - , 4 55. 3 - 1, 2 4 56. 5 - 5, - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, 5 6 57. 1 58. 3 - 4, 2 2 59. 5 - 3, 4 6 60. 3 - 6, 4 4 61. Domain: [0, 80], range: [0, 3200] 62. Domain: [0, 200], range: [0, 10] 63. (a) [25, 102]; (b) [0, 455]; (c) answers may vary. 64. (a) [0, 92.3]; (b) [0, 6,000,000]; (c) answers may vary. 65. (a) f 1 4 2 = 15.5; the charge for the first mile is $5, and then the charge for the next 3 mi is $3.50 each, giving a fare of $15.50 for a 4-mi trip; (b) f 1 4.25 2 = $19; the 0.25 mi is consid- ered part of a fourth additional mile after the first mile is charged at the $5 rate, so the total fare is $19.00 for a trip of at least 4 mi up to and including 5 mi. (c) The fares will be $5, $8.50, $12, and so on, in increments of $3.50, up to $36.50. Thus, the range is 5 5, 8.5, 12, 15.5, 19, 22.5, 26, 29.5, 33, 36.5 6 . 66. (a) S 1 95 2 = 20; it costs $20 to ship an order totaling $95; (b) S 1 102 2 = $15; it costs $15 1 $20 - $5 2 to ship an order totaling $102, since $2 is considered a part of an extra $20. (c) Orders totaling up to and including $120 will be shipped for $15; those totaling up to and including $140 will be shipped for $10; those totaling up to and including $160 will be shipped for $5. Thus, any order totaling $160.01 or more will be shipped for free. (d) The shipping charges are reduced in increments of $5. Thus, the range of S is 5 0, 5, 10, 15, 20 6 (the ordering of the elements does not matter). 67. 3 0, 5 2 68. 1 - ` , 0 2 < 1 0, 3 4 69. 1 - ` , - 3 2 < 1 - 3, 0 2 < 1 0, 3 2 < 1 3, ` 2 70. 1 - ` , - 3 2 < 1 - 3, 0 2 < 1 0, 4 2 < 1 4, ` 2 (b) 1 −1 −2 −4 −6 −2 −3 −4 2 3 4 10 12 14 16 8 6 4 2 x y f g (c) no 92. (a) f 1 x 2 = 1 x - 4 2 2 , g 1 x 2 = x 2 - 4; (b) 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y g f (c) no 93. h = 2 94. h = 9 Exercise Set R.3, p. 31 1. 1 - 1, 3 2 2. 3 - 2, 4 4 3. (0, 5) 4. 3 - 1, 2 4 5. 1 - 9, - 5 4 6. 3 - 9, - 4 2 7. 3 x , x + h 4 8. 1 x , x + h 4 9. 3 - 4, - 1 2 < 1 2, 3 4 10. 1 - ` , 0 2 < 3 3, ` 2 11. 3 - 2, 2 4 1 0 −1 −2 −3 −4 −5 2 3 4 5 12. 1 - 5, 5 2 1 0 −1 −2 −3 −4 −5 2 3 4 5 13. (6, 20] 12 0 2 4 6 8 10 14 16 18 20 14. 3 - 4, - 1 2 1 0 −1 −2 −3 −4 −5 2 3 4 5 15. 1 - 3, ` 2 1 0 −1 −2 −3 −4 −5 2 3 4 5 16. 1 - ` , - 2 4 1 0 −1 −2 −3 −4 −5 2 3 4 5 17. 1 - 2, 3 4 1 0 −1 −2 −3 −4 −5 2 3 4 5 18. 3 - 10, 4 2 2 0 −2 −4 −6 −8 −10 4 6 8 10 19. 3 - 4, - 3 2 < 1 0, 5 4 [ - 4, - 3) ´ (0, 5] 1 0 - 1 - 2 - 3 - 4 - 5 2 3 4 5 20. 1 - ` , - 2 2 < 3 1, 4 2 ( -q , - 2) ´ [1, 4) 1 0 - 1 - 2 - 3 - 4 - 5 2 3 4 5 21. (a) 3; (b) 5 - 3, - 1, 1, 3, 5 6 ; (c) 3; (d) 5 - 2, 0, 2, 3, 4 6 22. (a) - 1; (b) 5 - 4, - 3, - 2, - 1, 0, 1, 2 6 ; (c) - 2; (d) 5 - 2, - 1, 0, 1, 2, 3, 4 6 23. (a) 4; (b) 5 - 5, - 3, 1, 2, 3, 4, 5 6 ; (c) - 5, - 3, 4; (d) 5 - 3, 2, 4, 5 6 24. (a) 2; (b) 5 - 6, - 4, - 2, 0, 1, 3, 4 6 ; (c) 1, 3; (d) 5 - 5, - 2, 0, 2, 5 6 25. (a) - 1; (b) 3 - 2, 4 4 (c) 3; (d) 3 - 3, 3 4 26. (a) 2.5; (b) 3 - 3, 5 4 ; (c) 2; (d) [1, 4] 27. (a) - 2; (b) 3 - 4, 2 4 ; (c) - 2; (d) 3 - 3, 3 4 28. (a) About 2.3; (b) 3 - 4, 3 4 ; (c) 0; (d) 3 - 5, 4 4 29. (a) 3; (b) 3 - 3, 3 4 ; (c) at about - 1.4 and 1.4; (d) 3 - 5, 4 4 30. (a) 2; (b) 3 - 5, 4 4 ; (c) [1, 4]; (d) 3 - 3, 2 4 31. (a) 1; (b) 3 - 5, 5 2 ; (c) 3 3, 5 2 ; (d) 5 - 2, - 1, 0, 1, 2 6 32. (a) 2; (b) 3 - 4, 4 4 ; (c) 1 0, 2 4 ; (d) 5 1, 2, 3, 4 6 33. 1 - ` , 2 2 < 1 2, ` 2 ( -q , 2) ´ (2, q ) 2 34. 1 - ` , - 3 2 < 1 - 3, ` 2 ( -q , - 3) ´ ( - 3, q ) - 3 35. 3 0, ` 2 [0, q ) 0

  6. Page 6
    Read page 6 as text

    A N S W E R S A-5 71. Answers may vary. One example is f 1 x 2 = 1 x 1 x 2 - 4 2 . 72. Answers may vary. One example is f 1 x 2 = 1 x 1 x + 1 21 x - 7 2 . 73. Answers may vary. 74. 1 - ` , - 5 4 < 3 5, ` 2 75. 1 - ` , - 1 4 < 3 4, ` 2 76. Answers may vary. Technology Connection, p. 40 1. Graphs are left to the student. The two lines are parallel; y = x - 5 is shifted down 5 units from y = x . 2. Left to the student Exercise Set R.4, p. 44 11. m = 4, y @ intercept = 1 0, 1 2 12. m = 3, y @ intercept = 1 0, 6 2 13. m = - 2, y @ intercept = 1 0, 3 2 14. m = 2, y @ intercept = 1 0, 3 2 15. m = 1, y @ intercept = 1 0, 2 2 16. m = - 1, y @ intercept = 1 0, - 4 2 17. m = 1 3 , y @ intercept = a 0, - 7 3 b 18. m = - 1 4 , y @ intercept = a 0, 3 4 b 19. (a) y - 7 = 7 1 x - 1 2 ; (b) y = 7 x 20. (a) y + 3 = - 5 1 x + 2 2 ; (b) y = - 5 x - 13 21. (a) y - 3 = - 2 1 x - 2 2 ; (b) y = - 2 x + 7 22. (a) y + 2 = - 3 1 x - 5 2 ; (b) y = - 3 x + 13 23. (a) y - 0 = - 5 1 x - 5 2 ; (b) y = - 5 x + 25 24. (a) y - 0 = 2 1 x - 3 2 ; (b) y = 2 x - 6 25. (a) y + 6 = 1 2 1 x - 0 2 ; (b) y = 1 2 x - 6 26. (a) y - 7 = 4 3 1 x - 0 2 ; (b) y = 4 3 x + 7 27. (a) y - 8 = 0 # 1 x - 4 2 ; (b) y = 8 28. (a) y - 3 = 0 # 1 x - 2 2 ; (b) y = 3 29. (a) m = 2; (b) y = 2 x + 3; (c) (0, 3) 30. (a) m = 4; (b) y = 4 x - 19; (c) 1 0, - 19 2 31. (a) m = 1; (b) y = x + 4; (c) (0, 4) 32. (a) m = - 4; (b) y = - 4 x + 21; (c) (0, 21) 33. (a) m = 2 5 ; (b) y = 2 5 x - 19 5 (c) ¢ 0, - 19 5 ≤ 34. (a) m = 1 6 ; (b) y = 1 6 x + 23 6 ; (c) ¢ 0, 23 6 ≤ 35. (a) m = - 9 5 ; (b) y = - 9 5 x - 87 5 ; (c) ¢ 0, - 87 5 ≤ 36. (a) m = - 19 3 ; (b) y = - 19 3 x - 56 3 ; (c) ¢ 0, - 56 3 ≤ 37. (a) m = 0 ; (b) y = 6; (c) (0, 6); horizontal line 38. (a) m = 0 ; (b) y = - 1; (c) 1 0, - 1 2 ; horizontal line 39. (a) m = 0 ; (b) y = 0 ; (c) (0, 0); horizontal line 40. (a) m = 0 ; (b) y = 0 ; (c) (0, 0); horizontal line 41. (a) Undefined; (b) x = 4; (c) no y -intercept; vertical line 42. (a) Undefined; (b) x = - 6; (c) no y -intercept; vertical line 43. (a) Undefined; (b) x = 0 ; (c) all points on the y -axis are on this line, which is vertical. 44. (a) Undefined; (b) x = 0 ; (c) all points on the y -axis are on this line, which is vertical. 45. (a) m = 1 3 ; (b) y = 1 3 x - 1; (c) 1 0, - 1 2 46. (a) m = 15 4 ; (b) y = 15 4 x + 65 16 ; (c) ¢ 0, 65 16 ≤ 47. (a) m = 8 15 ; (b) y = 8 15 x + 1 15 ; (c) ¢ 0, 1 15 ≤ 48. (a) m = - 10 3 ; (b) y = - 10 3 x - 7 6 ; (c) ¢ 0, 7 6 ≤ 49. (a) m = 3 2 ; (b) y = 3 2 x + k - 3 2 h ; (c) ¢ 0, k - 3 2 h ≤ 50. (a) m = 1; (b) y = x + v - u + 3; (c) 1 0, v - u + 3 2 51. 0.4 5 = 0.08, or 8% 52. 2 5 = 0.4, or 40% 9. 1 −1 −1 −2 −2 −3 −4 −5 2 3 4 5 5 4 3 8 7 6 2 1 x y y = 7 m = 0 y -intercept: (0, 7) m = 0, y @ intercept = 1 0, 7 2 10. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = −5 m = 0 y -intercept: (0, −5) m = 0, y @ intercept = 1 0, - 5 2 1. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = −2 x m = −2 y -intercept: (0, 0) m = - 2, y @ intercept = 1 0, 0 2 2. m = −3 y -intercept: (0, 0) 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = −3 x m = - 3, y @ intercept = 1 0, 0 2 3. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y f ( x ) = −0.5 x m = −0.5 y -intercept: (0, 0) m = - 0.5, y @ intercept = 1 0, 0 2 4. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y f ( x ) = 0.5 x m = 0.5 y -intercept: (0, 0) m = 0.5, y @ intercept = 1 0, 0 2 5. m = 3 y -intercept: (0, −4) 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = 3 x − 4 m = 3, y @ intercept = 1 0, - 4 2 6. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = 2 x − 5 m = 2 y -intercept: (0, −5) m = 2, y @ intercept = 1 0, - 5 2 7. m = 1 y -intercept: (0, −2.5) 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y g ( x ) = x − 2.5 m = 1, y @ intercept = 1 0, - 2.5 2 8. m = −1 y -intercept: (0, 3) 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y g ( x ) = − x + 3 m = - 1, y @ intercept = 1 0, 3 2

  7. Page 7
    Read page 7 as text

    A-6 A N S W E R S 5. −2 −4 −6 −8 −10 −12 −14 −16 −1 −2 1 2 4 2 x y y = −3 x 2 y = −3 x 2 + 2 Domain: 1 - ` , ` 2 , or R , for both 6. −1 −2 −3 −4 −5 −6 −7 −8 −1 −2 1 2 2 1 x y y = −2 x 2 y = −2 x 2 + 1 Domain: 1 - ` , ` 2 , or R , for both (b) 4882; (c) answers may vary. 82. (a) N = 1.02 P ; (b) 204,000 people; (c) 360,000 people 83. (a) 19.7, 19.78, 20.5, 23.7, 24.5; (b) 25.3; (c) t A ( t ) 10 20 30 40 50 20 21 22 23 Age (in years) Number of years after 1950 24 25 60 A ( t ) = 0.08 t + 19.7 84. 25 85. Answers may vary. 86. (a) III; (b) IV; (c) I; (d) II 87. [0, 15] 88. Left to the student Technology Connection, p. 51 1. (a) 2, 4; (b) left to the student Technology Connection, p. 53 1. - 2, 1 2. 0, - 1.414, 1.414 3. 0, 700 4. - 2.079, 0.463, 3.116 5. - 0.387, 1.721 6. - 1.414, 1.414, 1, - 2 Technology Connection, p. 55 1. Left to the student 2. Left to the student Exercise Set R.5, p. 60 53. 43.33 1238 = 0.035, or 3.5% 54. 6 9 = 0.666 c , or about 66.7% 55. 55 100 = 0.55, or 55% 56. 87 100 = 0.87, or 87% 57. (a) T 1 w 2 = 0.000806 w ; (b) $2.98 58. (a) I 1 s 2 = 0.0057 s ; (b) 18 cartridges 59. (a) C 1 x 2 = 3 x + 1,000,000; (b) R 1 x 2 = 75 x ; (c) P 1 x 2 = 72 x - 1,000,000; (d) profit of $9,800,000; (e) 13,889 calculators - 10 6 3 * 10 6 2 * 10 6 10 6 0 y 10,000 20,000 R ( x ) C ( x ) P ( x ) x 60. (a) C 1 x 2 = 80 x + 45,000; (b) R 1 x 2 = 450 x ; (c) P 1 x 2 = 370 x - 45,000; (d) profit of $1,065,000; (e) 122 pairs R ( x ) C ( x ) P ( x ) $70,000 x y $35,000 −$35,000 100 200 300 400 500 61. (a) C 1 x 2 = 4 x + 250; (b) R 1 x 2 = 20 x ; $20 (c) 16 lawns 62. (a) C 1 x 2 = 5 x + 25,000; (b) R 1 x 2 = 25 x , $25; (c) 1250 tickets 63. (a) V 1 t 2 = 5200 - 512.5 t ; (b) V 1 0 2 = $5200, V 1 1 2 = $4687.50, V 1 2 2 = $4175, V 1 3 2 = $3662.50, V 1 4 2 = $3150, V 1 7 2 = $1612.50, V 1 8 2 = $1100 64. About $743,590 65. $25,200 66. (a) The number - 700 indicates that the value of the photo- copier decreases by $700 per year, and the number 3500 indicates that the original value of the copier was $3500. (b) 5 yr; (c) [0, 5], which means that after 5 yr, the value is 0 67. About 91% (don’t round up for legal reasons!) 68. About 33.3% 69. $682.75 70. $240.38 71. $161.89/yr 72. $2.56 billion/yr 73. (a) R = 4.17 T ; (b) 25 74. 0.02 sec 75. (a) M = 0.4 W ; (b) M = 40% W , which indicates that muscle weight is 40% of body weight; (c) 48 lb 76. (a) B = 0.025 W ; (b) B = 2.5% W , which indicates that brain weight is 2.5% of body weight; (c) 4 lb 77. (a) 115 ft, 75 ft, 135 ft, 179 ft. (b) For every increase of 1°F in the air temperature, the stopping distance increases by 2 ft. (c) Answers may vary. 78. (a) 6 ft, 11.5 ft, 22.5 ft, 55.5 ft, 72 ft; (b) r D ( r ) 10 10 20 30 20 30 D ( r ) = 11 r + 5 10 (c) For every 1-mph increase in speed, the braking distance increases by 1.1 ft. (d) Answers may vary. 79. (a) 145.78 cm; (b) 142.98 cm 80. (a) y = 263.5 x - 530,129.5; (b) 2140.5 million; (c) answers may vary. 81. (a) y = 289.75 x + 3143; 1. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = x 2 1 4 y = − x 2 1 4 Domain: 1 - ` , ` 2 , or R , for both 2. x y y = x 2 1 – 2 y = − x 2 1 – 2 –2 –1 1 2 –2 –1 1 2 Domain: 1 - ` , ` 2 , or R , for both 3. y = x 2 y = x 2 − 1 1 −1 −1 −2 −3 −2 −3 −4 −5 2 3 4 5 5 4 7 6 3 2 1 x y Domain: 1 - ` , ` 2 , or R , for both 4. y = x 2 y = x 2 − 3 1 −1 −1 −2 −3 −2 −3 −4 −5 2 3 4 5 5 4 7 6 3 2 1 x y Domain: 1 - ` , ` 2 , or R , for both

  8. Page 8
    Read page 8 as text

    A N S W E R S A-7 7. 2 −2 −2 −4 −6 −8 −10 −4 −6 −8 −10 4 6 8 10 10 8 6 4 2 x y y = | x − 3| y = | x | Domain: 1 - ` , ` 2 , or R , for both 8. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = x − 1 y = x Domain: 1 - ` , ` 2 , or R , for both 9. y = | x | 0 - 5 - 5 - 10 5 x y 5 y = | x + 2| + 1 10 10 Domain: 1 - ` , ` 2 , or R , for both 10. 0 - 5 5 x y 5 - 5 y = | x - 3| - 4 y = | x | - 10 10 10 Domain: 1 - ` , ` 2 , or R , for both 11. x y y = x 3 + 1 –2 –1 1 2 –8 –4 –1 1 4 8 y = x 3 Domain: 1 - ` , ` 2 , or R , for both 12. −2 −4 −6 −8 −10 −1 −2 1 2 10 8 6 4 2 x y y = x 3 y = x 3 + 2 Domain: 1 - ` , ` 2 , or R , for both 13. 1 2 3 4 5 1 2 3 x y x − 1 y = x y = Domains: 3 0, ` 2 and 3 1, ` 2 14. y 1 2 3 4 5 6 1 2 3 x x −2 y = x y = Domains: 3 0, ` 2 and 3 2, ` 2 15. x + 2 - 1 y = x y = x y - 2 - 1 1 2 - 1 1 Domains: 3 0, ` 2 and 3 - 2, ` 2 16. y 0 5 x 5 10 x - 3 + 4 y = x y = Domains: 3 0, ` 2 and 3 3, ` 2 17. (a) 1 - 2, - 1 2 , x = - 2; (b) opens upward; (c) 1 - 3, 0 2 , 1 - 1, 0 2 18. (a) 1 3, - 4 2 , x = 3; (b) opens upward; (c) (1, 0), (5, 0) 19. (a) 1 - 4, - 16 2 , t = - 4; (b) opens upward; (c) 1 - 8, 0 2 , (0, 0) 20. (a) 1 - 6, 36 2 , t = - 6; (b) opens downward; (c) 1 - 12, 0 2 , (0, 0) 21. (a) ¢ 1 4 , 33 8 ≤ , s = 1 4 ; (b) opens downward; (c) ¢ 1 - 2 33 4 , 0 ≤ , ¢ 1 + 2 33 4 , 0 ≤ 22. (a) ¢ 1 3 , 7 3 ≤ , r = 1 3 ; (b) opens downward; 25. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y 3 x y = Domain: 1 - ` , 0 2 < 1 0, ` 2 26. –4 –3 –2 –1 1 2 3 4 –4 –3 –2 –1 1 2 3 4 y = 2 – x x y Domain: 1 - ` , 0 2 < 1 0, ` 2 27. – 4 – 3 – 2 – 1 1 2 3 4 – 4 – 3 – 2 – 1 1 2 3 4 y = – 2 – x x y Domain: 1 - ` , 0 2 < 1 0, ` 2 28. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y 3 x y = − Domain: 1 - ` , 0 2 < 1 0, ` 2 (c) ¢ 1 - 2 7 3 , 0 ≤ , ¢ 1 + 2 7 3 , 0 ≤ 23. (a) ¢ - 6 5 , - 121 50 ≤ , x = - 6 5 ; (b) opens upward; (c) ¢ - 17 5 , 0 ≤ , 1 1, 0 2 24. (a) ¢ - 3 5 , - 64 75 ≤ , x = - 3 5 ; (b) opens upward; (c) ¢ - 11 5 , 0 ≤ , 1 1, 0 2 29. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = 1 x − 1 Domain: 1 - ` , 1 2 < 1 1, ` 2 30. – 2 – 1 1 2 1 2 3 4 x y y = 1 — x 2 Domain: 1 - ` , 0 2 < 1 0, ` 2 31. – 4 – 3 – 2 – 1 1 2 3 4 – 2 1 2 – 1 x y 3 x y = Domain: 1 - ` , ` 2 , or R 32. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = 1 x Domain: 1 - ` , 0 2 < 1 0, ` 2 33. 1 −1 −1 −2 −3 −2 −3 −4 −5 −6 −7 −8 2 5 4 7 6 3 2 1 x y g ( x ) = x 2 + 7 x + 10 x + 2 Domain: 1 - ` , - 2 2 < 1 - 2, ` 2 34. 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 −6 −7 2 3 5 4 3 2 1 x y f ( x ) = x 2 + 5 x + 6 x + 3 Domain: 1 - ` , - 3 2 < 1 - 3, ` 2

  9. Page 9
    Read page 9 as text

    A-8 A N S W E R S 90. (a) 1.93 m 2 ; (b) 1.88 m 2 ; (c) h f(h ) 100 200 1 2 f(h ) = 0.144 h 1/2 91. 26, 51 92. Answers may vary. 93. Answers may vary. 94. 0, 1, - 1 95. - 1.831, - 0.856, 3.188 96. 1.5, 9.5 97. 1.489, 5.673 98. - 2.449, 2.449 99. - 2, 3 100. No zeros 101. 3 - 1, 2 4 102. - 10.153, - 1.871, - 0.821, - 0.303, 0.098, 0.535, 1.219, 3.297 103. 1 + 2 5 2 104. 1 + 2 5 2 105. 1 + 2 5 2 106. All three problems translate into the same equation: x 2 - x - 1 = 0. Exercise Set R.6, p. 72 1. (a) x - 3 - 2 - 1 0 1 2 3 f 1 x 2 = 4 x 0.0156 0.0625 0.25 1 4 16 64 (b) 300%; (c) (0, 1); (d) x y 16 14 12 10 8 6 4 2 1 - 1 - 2 2 y = 4 x 2. (a) x - 3 - 2 - 1 0 1 2 3 g 1 x 2 = 5 x 0.008 0.04 0.2 1 5 25 125 (b) 400%; (c) (0, 1); (d) y 30 24 27 21 18 15 12 9 6 3 2 1 x - 2 - 1 y = 5 x 3. (a) x - 3 - 2 - 1 0 1 2 3 h 1 x 2 = 2 # 1.5 x 0.5926 0.8889 1.3333 2 3 4.5 6.75 (b) 50%; (c) (0, 2); (d) y = 2 – 1.5 x 1.0 2.0 - 2.0 - 1.0 2 1 4 3 5 x y 35. x = 1 { 2 3 36. x = 1 { 2 5 37. x = - 3 { 2 10 38. x = - 2 { 2 7 39. x = 1 { 2 2 2 40. x = - 1 { 2 2 2 41. y = - 4 { 2 10 3 42. p = 5 { 2 33 4 43. x = - 7 { 2 13 2 44. w = 1 { 2 5 2 45. 2 5 x 46. 2 7 t 47. 2 3 y 2 48. 2 5 t 2 49. 1 2 5 t 2 50. 1 2 3 y 2 51. 1 2 3 b 52. 1 2 5 b 53. 1 2 x 2 + 3 54. 1 2 4 y 2 + 7 55. x 3/2 , x Ú 0 56. x 5/2 , x Ú 0 57. a 3/ 5 58. b 1/2 , b Ú 0 59. x 3 , x Ú 0 60. t 2 61. t - 5/2 , t ? 0 62. m - 2 , m ? 0 63. 1 x 2 + 7 2 - 1/2 64. 1 x 3 + 4 2 1/2 65. 27 66. 1024 67. 16 68. 4 69. 1 - ` , 5 2 < 1 5, ` 2 70. 1 - ` , - 2 2 < 1 - 2, ` 2 71. 1 - ` , 2 2 < 1 2, 3 2 < 1 3, ` 2 72. 1 - ` , - 5 2 < 1 - 5, - 1 2 < 1 - 1, ` 2 73. J - 4 5 , ` ≤ 74. 3 3, ` 2 75. 1 - ` , 7 4 76. 1 - ` , 5 4 77. (50, 500); quantity = 50, price = $ 500 78. (40, 7600); quantity = 40, price = $ 7600 79. (5, 1); quantity = 5000, price = $ 100 80. (4, 1); quantity = 4000, price = $ 100 81. (1, 4); quantity = 100, price = $ 4 82. (1, 9); quantity = 100, price = $ 9 83. (2, 3); quantity = 2000, price = $ 3000 84. (3, 4); quantity = 3000, price = $ 4000 85. 140 tickets 86. 120,000 87. (a) 166 mi, 176 mi, 184 mi; (b) x R ( x ) R ( x ) = 11.74 x 0.25 40,000 80,000 20 40 60 80 100 120 140 160 180 200 88. 64.2, 93.3, 121.6, 149.3, 176.5, 203.4; w H ( w ) H ( w ) = 0.059 w 0.92 4000 8000 2000 6000 50 100 150 200 250 89. (a) 10.43 o g/m 3 ; 10.20 o g/m 3 ; 10.03 o g/m 3 ; (b) t 10 20 30 40 50 p ( t ) 2 4 6 8 10 12 14 p ( t ) = 12.85 t −0.077

  10. Page 10
    Read page 10 as text

    A N S W E R S A-9 4. (a) x - 3 - 2 - 1 0 1 2 3 k 1 x 2 = 6 # 1.2 x 3.4722 4.1667 5 6 7.2 8.64 10.368 (b) 20%; (c) (0, 6); (d) y = 6 – 1.2 x 5 - 5 4 6 8 10 12 2 16 14 20 18 x y 1 2 3 4 - 4 - 3 - 2 - 1 5. (a) x m 1 x 2 = - 3 # 2.15 x - 3 - 0.3019 - 2 - 0.649 - 1 - 1.3953 0 - 3 1 - 6.45 2 - 13.8675 3 - 29.8151 (b) 115%; (c) 1 0, - 3 2 ; (d) y = - 3 – 2.15 x 1 2 - 2 - 1 - 14 - 12 - 6 - 8 - 10 - 2 - 4 x y 6. (a) x n 1 x 2 = - 2 # 3.04 x - 3 - 0.0712 - 2 - 0.2164 - 1 - 0.6579 0 - 2 1 - 6.08 2 - 18.4832 3 - 56.1889 (b) 204%; (c) 1 0, - 2 2 ; (d) y = - 2 – 3.04 x 1 2 - 2 - 1 - 15 - 5 - 10 x y 7. (a) x p 1 x 2 = 12,000 1 0.95 2 x - 3 13,996.2094 - 2 13,296.3989 - 1 12,631.579 0 12,000 1 11,400 2 10,830 3 10,288.5 (b) - 5%; (c) (0, 12,000); (d) y = 12,000(0.95) x 4 3 2 1 5 - 5 - 1 - 2 - 3 - 4 10,000 5000 15,000 20,000 x y 0 8. (a) x q 1 x 2 = 75,000,000 1 0.875 2 x - 3 111,953,352.8 - 2 97,959,183.7 - 1 85,714,285.7 0 75,000,000 1 65,625,000 2 57,421,875 3 50,244,140.6 (b) - 12.5%; (c) (0, 75,000,000); (d) y = 75,000,000(0.875) x 100,000,000 150,000,000 200,000,000 y 5 1 2 3 4 - 5 - 4 - 3 - 2 - 1 x 50,000,000 9. (a) x r 1 x 2 = r 0 1 0.233 2 x - 3 79.0555 r 0 - 2 18.4199 r 0 - 1 4.2918 r 0 0 r 0 1 0.233 r 0 2 0.0543 r 0 3 0.0126 r 0 (b) - 76.7%; (c) 1 0, r 0 2 ; (d) y = r 0 (0.233) x r 0 1 2 - 2 - 1 x y

  11. Page 11
    Read page 11 as text

    A-10 A N S W E R S 77. (a) A 1 t 2 = 900 1 1.045 2 t ; (b) A 1 5 2 = 1121.56, which means that in 2020 the student population will be about 1122; (c) after 6.54 yr (or in 2021) 78. (a) P 1 t 2 = 12,500 1 1.0275 2 t ; (b) P 1 8 2 = 15,529.76, which means that in 2023 the population of Parker Valley will be about 15,530; (c) after 17.3 yr, or in 2032 79. (a) M 1 t 2 = 50 1 0.9875 2 t ; (b) M 1 15 2 = 41.4, which means that after 15 days the mass of the sample is 41.4 mg; (c) after 72.8 days 80. (a) q 1 t 2 = 2500 1 0.976 2 t ; (b) q 1 11 2 = 1913.76, which means that in 2022 the population of Tonopah Acres will be 1914; (c) after 28.5 yr, or in 2039 81. (a) E 1 t 2 = 550 1 1.471 2 t ; (b) E 1 10 2 = 26,090.92, which means that in 10 years there will be about 26,091 students enrolled in the online program; (c) after 5.72 yr (in the 6th year) 82. (a) G 1 t 2 = 15 1 1.222 2 t ; (b) G 1 12 2 = 166.3, which means that after 12 months the company will have about 166 employees; (c) after 14 months 83. In 28.1 yr 84. In 37.2 yr 85. After 10.5 weeks 86. After 6 months 87. Left to the student 88. Left to the student 89. Left to the student 90. Left to the student 91. 80 90 7 90 80 92. 125 200 7 200 125 93. 1 - ` , - 1 2 < 1 1, ` 2 Technology Connection, p. 79 1. (a) Left to the student; (b) 93.5; (c) left to the student Technology Connection, p. 81 1. y = 0.0016278847 x 4 - 0.1814259451 x 3 + 6.716198092 x 2 - 91.87760958 x + 397.9916923; the fit of this equation is slightly better. 2. Graphs are left to the student. (a) y = - 58.21428571 x 2 + 5258.214286 x - 45,399.19643; (b) y = - 0.305555555 x 3 - 17.42261905 x 2 + 3597.290675 x - 25,339.89435; (c) y = 0.00416666666 x 4 - 1.047222222 x 3 + 29.25625 x 2 + 2380.242163 x - 14,388.75272; (d) quartic; (e) $48,667, $73,624 Exercise Set R.7, p. 82 1. Linear 2. Quadratic with a 7 0 or exponential with 0 6 a 6 1 3. Quadratic with a 6 0 4. Polynomial, neither quadratic nor linear 5. Quadratic with a 7 0 6. Linear, possibly polynomial 7. Linear 8. Quadratic with a 7 0 9. Exponential with 0 6 a 6 1 10. (a) y = 0.1167 x + 5.1; (b) $6.03 million, $6.62 million; (c) in 2028 11. (a) y = 0.933 x + 63.2; (b) $71.6 billion 12. (a) y = - 44.333 x 2 + 188.667 x ; (b) 45.3 mg; (c) answers may vary. 13. (a) y = 237.5 x 2 - 1400 x + 54,762.5 (b) $64,512.50 14. (a) y = 0.144 x 2 - 4.63 x + 60; (b) about 188.5 ft; (c) answers may vary. 10. (a) x s 1 x 2 = s 0 1 0.752 2 x - 3 2.3515 s 0 - 2 1.7683 s 0 - 1 1.3298 s 0 0 s 0 1 0.752 s 0 2 0.5655 s 0 3 0.4253 s 0 (b) - 24.8%; (c) 1 0, s 0 2 ; (d) y = s 0 (0.752) x s 0 1 2 - 2 - 1 x y 11. l og 4 64 = 3 12. l og 5 625 = 4 13. log 10 0.01 = - 2, or log 0.01 = - 2 14. log 7 ¢ 1 49 ≤ = - 2 15. log 25 5 = 1 2 16. log 36 6 = 1 2 17. log 216 6 = 1 3 18. log 32 2 = 1 5 19. log P Q = n 20. l og r z = v 21. 2 7 = 128 22. 4 5 = 1024 23. 10 7 = 10,000,000 24. 10 5 = 100,000 25. 16 1/2 = 4 26. 100 1/2 = 10 27. 7 1/3 = 2 3 7 28. 15 1/4 = 2 4 15 29. 9 0 = 1 30. p 0 = 1 31. 256 32. 1024 33. 5 34. 8 35. 1 36. 1 37. - 2 38. - 2 39. p 40. 2 2 41. 2.80735 42. 1.29203 43. 2.52372 44. 1.35621 45. 2.32193 46. 1.63563 47. 1.73249 48. 3.16993 49. 0.61315 50. 0.31546 51. 1.71241 52. 1.45816 53. 2.43068 54. 1.88562 55. 10.76961 56. 39.16960 57. 1.89620 58. 3.78878 59. 1.03018 60. 1.09369 61. 1.449 62. 1.532 63. 1.732 64. 2.015 65. 0.283 66. 1.049 67. 1.966 68. 2.249 69. - 0.483 70. - 0.766 73. y = log 4 ( x - 3) y - 1 x 1 2 4 7 2 3 1 10 9 8 6 5 - 2 - 3 5 x u x 7 3 6 74. 1 - 1 - 1 - 2 - 3 - 2 - 3 - 4 - 6 2 3 4 6 5 3 1 x y 2 y = log 3 ( x + 5) 5 x u x 7 - 5 6 71. 20 12 14 16 18 2 4 6 8 10 x y - 1 2 3 1 y = log 3 x - 2 5 x u x 7 0 6 72. 20 12 14 16 18 2 4 6 8 10 x y - 1 2 3 1 - 2 y = log 5 x 5 x u x 7 0 6 75. 1 2 3 4 5 6 7 8 9 10 - 1 - 2 2 x y 1 y = log(2 x - 1) b x u x 7 1 2 r 76. 2 3 4 1 5 - 5 - 4 - 3 - 1 - 2 - 1 - 2 2 x y 1 y = log 2 (2 - 3 x ) b x u x 6 2 3 r

  12. Page 12
    Read page 12 as text

    A N S W E R S A-11 15. (a) y = 1.491 x - 33.549; (b) 41%; (c) the estimate is higher than the actual value. 16. (a) y = 1.274 x - 25.309; (b) about 26%; (c) the estimate is slightly higher than the actual value. 17. (a) y = 11.42 1 1.02 2 x ; (b) 33.9 million 18. (a) y = 1.467 1 0.983 2 x ; (b) 0.57 million 19. (a) y = 108.708 1 1.03 2 x ; (b) $354.62; (c) answers may vary. 20. (a) y = 26.246 1 1.189 2 x ; (b) $148.21; (c) answers may vary. 21. Answers may vary. 22. Answers may vary. 23. (a) 2, 3 2 , 1, so the average slope is 1.5; (b) y = 1.5 x - 1.166666 . . . ; (c) they are the same. 24. Answers may vary. 25. (a) y = 0.00648 x 2 - 0.884 x + 33.217; (b) 5.2; (c) y = 24.068 1 0.975 2 x , which gives an estimate of about 6.9; (d) answers may vary. 26. (a) y = - 0.278 x 4 + 4.929 x 3 - 30.271 x 2 + 73.18 x + 15.757 (b) - $127.5 million; (c) answers may vary. 27. (a) Equation (4) is - 24 a - 2 b = 495; (b) equation (5) is 32 a + 2 b = 341; (c) a = 836 8 = 104.5; (d) b = - 3003 2 = - 1501.5; (e) c = 6016 Chapter R Review Exercises, p. 93 1. (d) 2. (b) 3. (f) 4. (a) 5. (e) 6. (g) 7. (h) 8. (c) 9. True 10. False 11. True 12. True 13. False 14. False 15. True 16. (a) 4.1 million; (b) 32 and 85; (c) [0, 92.3] 17. $4177.94 18. $13,402.43 19. No. Elizabeth (input) has three outputs. 20. (a) - 6; (b) - 30; (c) - a 2 + a ; (d) - x 2 - 2 xh - h 2 + x + h 21. f ( x ) = ( x − 2) 2 1 −1 −1 −2 −3 −4 −5 2 3 4 5 5 4 7 6 9 8 3 2 1 x y 22. 1 − 1 − 1 − 2 − 3 − 4 − 5 − 2 − 3 − 4 − 5 2 3 4 5 5 4 3 2 1 x y y = | x − 1 | 23. - 10 10 3 - x x + 4 f ( x ) = y x - 20 - 10 10 20 24. x + 1 g ( x ) = 1 −1 −1 −2 −3 −4 −5 2 3 4 5 6 7 8 9 5 4 3 2 1 x y 25. No 26. Yes 27. Yes 28. No 29. (a) 1; (b) 3 - 4, 4 4 ; (c) - 3; (d) 3 - 1, 3 4 30. (a) 1, 4, 3; (b) 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = f ( x ) 31. (a) 3 - 2, 5 4 ; (b) 1 - 1, 3 4 ; (c) 1 - ` , a 2 ; (d) 1 - ` , - 1 4 < 3 3, 4 2 32. (a) 3 - 4, 5 2 1 0 −1 −2 −3 −4 −5 2 3 4 5 (b) (2, ` ) 1 0 −1 −2 −3 −4 −5 2 3 4 5 33. (a) - 2; (b) 5 - 3, - 2, - 1, 0, 1, 2, 3 6 ; (c) 5 - 1, 3 6 ; (d) 5 - 2, 1, 2, 3, 4 6 34. (a) 1 - ` , 5 2 < 1 5, ` 2 ; (b) 3 - 6, ` 2 ; (c) 1 2, ` 2 ; (d) [0, 5] 35. Slope: - 3, y -intercept: (0, 2) 36. y = 1 4 x - 7 37. - 3 38. - $350 > yr 39. 75 pages/day 40. A = 0.1 V (c) 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y 1 x y = − (d) 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = x 2 + x − 6 x − 2 44. (a) x = 1, x = 3; (b) x = 2 { 2 10 2 45. (a) x 4/5 ; (b) t 4 ; (c) m - 2/3 ; (d) 1 x 2 - 9 2 - 1/2 46. (a) 2 5 x 2 ; (b) 1 2 5 m 3 ; (c) 2 x 2 - 5; (d) 2 3 t 47. J 9 2 , ` ≤ 48. (a) 1 −1 −1 −2 −3 −4 2 3 4 5 x 5 4 3 2 1 y y = • (4) x 1 2 0, ) ( 1 2 (b) 1 −1 −1 −2 2 3 4 5 x 5 4 3 2 1 y y = 3 • x ) ) 1 4 (0, 3) 49. (a) 2.3%; (b) 25,209, which means that in 2023 the popula- tion of Arvon Hill will be 25,209; (c) after 19.4 yr, or in 2037 50. (a) M 1 t 2 = 125 1 0.986 2 t ; (b) - 1.4%/week; (c) after 65 weeks 51. (a) 1.256; (b) 0.183; (c) 1.497 52. 4, which is the power to which 3 must be raised to give 81 53. (3, 16); quantity = 300, price = $ 16 54. About 3.3 hr 41. (a) C 1 x 2 = 0.5 x + 4000; x y R ( x ) C ( x ) P ( x ) 4000 6000 $8000 2000 −4000 −2000 200 400 600 (b) R 1 x 2 = 10 x ; (c) P 1 x 2 = 9.5 x - 4000; (d) 422 CDs 42. (a) x − 3 y = x y = 1 −1 −1 −2 −3 −4 −5 2 3 4 5 6 7 8 9 5 4 3 2 1 x y (b) 1 −1 −1 −2 −3 −4 −5 −2 −3 −4 −5 2 3 4 5 5 4 3 2 1 x y y = x 3 y = ( x − 1) 3 43. (a) 1 −1 −1 −2 2 3 4 5 6 7 8 x y f ( x ) = x 2 − 6 x + 8 5 4 7 8 9 6 3 2 1 vertex: 1 3, - 1 2 (b) 2 −2 −1 −2 −3 −4 −5 −4 −6 −8 −10 4 6 8 10 5 4 3 2 1 x y x + 2 3 g ( x ) =

  13. Page 13
    Read page 13 as text

    A-12 A N S W E R S 14. 4 8 12 –8 –4 –12 –4 –8 –12 12 8 4 x y f ( x ) = 8 x 15. t - 1/2 16. 1 2 5 t 3 17. - 1 2 18. 20 10 30 - 10 4 6 2 x y x - 4 + 1 f ( x ) = 19. 3 c , d 2 20. 1 - 2, ` 2 21. 1 - ` , - 7 2 < 1 - 7, 2 2 < 1 2, ` 2 22. – 3 – 2 – 1 1 2 3 – 3 – 2 – 1 1 2 3 4 5 x 2 + 2, for x ≥ 0 e x 2 – 2, for x < 0 f ( x ) = 23. 1 −1 −1 −2 −3 2 3 4 5 x 5 4 3 2 1 y f ( x ) = • (3) x 1 2 0, ) ( 1 2 ¢ 0, 1 2 ≤ 24. (a) 4.1%/yr; (b) after 10.09 yr 25. (a) x 10 20 30 40 y 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 (b) Yes; (c) y = - 1.94 x 2 + 102.74 x + 1253.49; (d) About 2590 calories; (e) answers may vary. 26. 1 16 27. Domain: ¢ - ` , 5 3 R , x -intercept: ¢ - 798 2 3 , 0 ≤ 28. One possible equation is y = 1 x + 3 21 x - 1 21 x - 4 2 . 29. 51 7 30. |9 – x 2 | – 1 3 y = –10 10 12 –12 Zeros: { 2 8, { 2 10 ; domain: 1 - ` , ` 2 ; range: 3 - 1, ` 2 31. (a) y = - 1.51 x 2 + 79.98 x + 1436.93; (b) about 2480 calories; (c) answers may vary. 55. (a) M = 0.2 r + 160 (b) r 50 60 70 80 M = 0.2 r + 160 M 170 171 172 173 174 175 176 177 (c) 173.4 beats/min 56. (a) Left to the student; (b) yes; (c) P = 1.9975 x 2 - 89.8444 x + 870; (d) about - $27.56; (e) answers may vary. 57. (a) 525,375 lb; (b) $4.31/lb 58. 3 - 5, 5 4 59. [1, 2] 60. a = - 1 2 61. −10 10 400 −400 y = x 3 − 9 x 2 + 27 x + 50 x = - 1.25; domain and range: 1 - ` , ` 2 62. |4 − x 2 | + 1 3 y = −10 10 6 −1 no zeros; domain: 1 - ` , ` 2 , range: 3 1, ` 2 63. 1 - 1.21, 2.36 2 64. (a) P = 1.86 x 2 - 84.18 x + 943.86; (b) $95.46; (c) answers may vary. 65. (a) Linear: A = - 9.190819894 x + 697.05481; quadratic: A = 0.0757317559 x 2 - 15.51100944 x + 801.4311225; cubic: A = 0.0052352573 x 3 - 0.5849501976 x 2 + 9.082584281 x + 545.8186828; exponential: A = 1014.883046 1 0.9677603597 2 x ; (b) 800 0 80 0 y 1 = 29.190819894 x + 697.05481 y 2 = 0.0757317559 x 2 − 15.51100944 x + 801.4311225 y 3 = 0.0052352573 x 3 − 0.5849501976 x 2 + 9.082584281 x + 545.8186828 y 4 = 1014.883046(0.9677603597) x y 1 y 2 y 3 y 4 (c) Answers may vary. Chapter R Test, p. 97 1. $750 2. (a) - 4; (b) - x 2 - 2 xh - h 2 + 5 3. m = 4 5 ; y @ intercept: ¢ 0, - 2 3 ≤ 4. y = 1 4 x + 31 4 5. - 1 2 6. - $ 700/yr; 7. 1 2 lb/bag 8. F = 2 3 W 9. (a) C 1 x 2 = 0.08 x + 8000; (b) R 1 x 2 = 0.50 x ; (c) P 1 x 2 = 0.42 x - 8000; (d) 19,048 cards 10. (3, 25); quantity = 3000, price = $ 25 11. Yes 12. No 13. (a) - 4; (b) 1 - ` , ` 2 ; (c) 5 - 3, 3 6 ; (d) 3 - 5, ` 2

  14. Page 14
    Read page 14 as text

    A N S W E R S A-13 Extended Technology Application, p. 99 1. (a) P 1 t 2 = 0.1267032967 t - 0.5842857143; (b) y 1 0 70 10 0 (c) $8.28, $8.92, answers may vary; (d) 2112, which seems too far into the future. 2. (a) P 1 t 2 = 0.0014796703 t 2 + 0.0305247253 t + 0.3775; (b) y 2 0 70 10 0 (c) $9.76, $10.99, answers may vary; (d) 2055, which is plausible. 3. (a) P 1 t 2 = - 0.00000183 t 3 + 0.0016588147 t 2 + 0.0260369288 t + 0.3972058824; (b) y 3 0 70 10 0 (c) $9.72, $10.91, answers may vary; (d) 2057, which is also plausible. 4. (a) P 1 t 2 = 0.00000046249829 t 4 - 0.00006196216 t 3 + 0.004115011 t 2 - 0.006602236 t + 0.4680672269; (b) y 4 0 70 10 0 (c) $10.02, $11.61, answers may vary; (d) 2042, which is plausible, but may be too soon. 5. (a) P 1 t 2 = 0.5430389024 1 1.047332533 2 t ; (b) y 5 0 70 10 0 (c) $13.83, $17.43, answers may vary; (d) 2028, which is probably too soon. 6. Answers may vary.

  15. Page 15
    Read page 15 as text

    A N S W E R S A-63 ANSWERS: DIAGNOSTIC TEST, p. xvii Part A The red bracketed references indicate where worked-out solutions can be found in Appendix A: Review of Basic Algebra. For example, [Ex. 1] means that the problem is worked out in Example 1 of the appendix. 1. 64 [Ex. 1] 2. - 32 [Ex. 1] 3. 1 8 [Ex. 1] 4. - 2 x [Ex. 2] 5. 1 [Ex. 2] 6. 1 x 5 [Ex. 3] 7. 16 [Ex. 3] 8. 1 t [Ex. 3] 9. x 11 [Ex. 4] 10. x 7 [Ex. 4] 11. 40 x 3 [Ex. 4] 12. a [Ex. 5] 13. b 8 [Ex. 5] 14. 1 x 6 [Ex. 6] 15. y 1 5 8 x 12 z 9 [Ex. 6] 16. 3 x - 15 [Ex. 7] 17. x 2 - 2 x - 15 [Ex. 7] 18. a 2 + 2 ab + b 2 [Ex. 7] 19. 4 x 2 - 4 xt + t 2 [Ex. 8] 20. 9 c 2 - d 2 [Ex. 8] 21. h 1 2 x + h 2 [Ex. 9] 22. 1 x - 3 y 2 2 [Ex. 9] 23. 1 x + 2 21 x - 7 2 [Ex. 9] 24. 1 2 x - 1 21 3 x + 5 2 [Ex. 9] 25. 1 x - 7 21 x + 2 21 x - 2 2 [Ex. 10] 26. x = 6 [Ex. 11] 27. x = 0, 2, - 4 5 [Ex. 12] 28. x = 0, 1 2 , - 1 2 [Ex. 13] 29. No solution [Ex. 15] 30. x … 21 13 or 1 - ` , 21 13 4 [Ex. 17] 31. 660 lb [Ex. 19] 32. 199 suits [Ex. 20] Part B The red bracketed references indicate where worked-out solutions can be found in Chapter R. For example, [Ex. R.2.5] means that the problem is worked out in Example 5 of Section R.2. 1. 2 4 2 2 2 4 2 2 2 4 2 4 x y y 5 2 x 1 1 [Ex. R.1.1] 2. 2 4 2 2 2 4 2 2 4 2 6 x y 3 x 1 5 y 5 10 [Ex. R.1.2] 3. y 5 x 2 2 1 2 4 2 2 2 4 2 2 4 2 6 8 x y [Ex. R.1.3] 4. 6 4 8 2 2 2 2 4 2 4 x y x 5 y 2 [Ex. R.1.4] 5. g 1 0 2 = 8; g 1 - 5 2 = 143; g 1 7 a 2 = 147 a 2 - 14 a + 8 [Ex. R.2.4] 6. x = 4 [Ex. R.2.4] 7. 2 1 3 2 1 3 2 1 2 2 4 2 2 2 1 x y f ( x ) 5 4, 3 2 x 2 , 2 x 2 6, for x $ 0, for 0 , x # 2, for x . 2. [Ex. R.2.8] 8. 1 - 4, 5 2 [Ex. R.3.1a] 9. 5 x u x is any real number and x ? 5 2 6 or 1 - ` , 5 2 2 h 1 5 2 , ` 2 [Ex. R.3.5] 10. Slope m = 1 2 ; y -intercept: 1 0, - 7 4 2 [Ex. R.4.6] 11. y = 3 x - 2 [Ex. R.4.7] 12. m = - 3 2 [Ex. R.4.1] 13. x = 5 [Ex. R.6.7] 14. x = - 2 [Ex. R.6.7] 15. 2 4 6 2 2 2 4 2 2 4 2 x y f ( x ) 5 x 2 2 2 x 2 3 2 4 [Ex. R.5.1] 16. 2 4 2 2 2 4 2 2 2 4 2 4 x y g ( x ) 5 x 3 [Ex. R.5.4] 17. 2 4 2 2 2 4 2 2 2 4 2 4 x y f ( x ) 5 1 x [Ex. R.5.5] 18. f ( x ) 5 | x | 2 4 2 2 2 4 2 2 4 2 6 x y [Ex. R.5.7] 19. f ( x ) 5 2 √ x 6 4 8 2 2 2 2 4 2 6 2 x y [Ex. R.5.8] 20. $1102.50 [Ex. R.1.6]

  16. Page 16
    Read page 16 as text

    A-14 A N S W E R S 69. 1 - 1 - 1 - 2 - 3 - 2 2 3 4 5 6 7 8 5 4 7 6 3 2 1 x y g ( x ) = 2 x - 5 x - 3 2, does not exist 70. 1 - 1 - 1 - 2 - 3 - 4 - 5 - 6 - 7 2 3 5 4 3 2 9 8 7 6 1 x y g ( x ) = 4 x + 9 x + 2 4, does not exist ANSWERS: CHAPTER 1 Exercise Set 1.1, p. 112 1. 0.3, x S 0.3 - 2. 1.7, x S 1.7 + 3. - 3, x S - 3 - 4. - 4.9, x S - 4.9 + 5. 2 3 , x S 1 2 3 2 - 6. 4 3 , x S 1 4 3 2 - 7. 0.3, x S 0.3 - 8. 1.2, x S 1.2 - 9. 1, x S 1 + 10. 0, x S 0 - 11. - 2 12. 7 13. l im x S 2 + 14. l im x S 3 - 15. l im x S 5 16. lim x S 1 2 17. “the limit, as x approaches 4, of f 1 x 2 ” or “the limit of f 1 x 2 as x approaches 4” 18. “the limit, as x approaches 1, of g 1 x 2 ” or “the limit of g 1 x 2 as x approaches 1” 19. “the limit, as x approaches 5 from the left, of F 1 x 2 ” or “the limit of F 1 x 2 as x approaches 5 from the left” 20. “the limit, as x approaches 4 from the right, of G 1 x 2 ” or “the limit of G 1 x 2 as x approaches 4 from the right” 21. (a) - 3; (b) - 3; (c) - 3 22. (a) 1; (b) 2; (c) does not exist 23. (a) - 1; (b) - 1; (c) - 1 24. (a) 4; (b) 2; (c) does not exist 25. 5 26. 4 27. Does not exist 28. 0 29. 2 30. 0 31. 2 32. 4 33. 1 34. 3 35. 4 36. - 1 37. 0 38. Does not exist 39. 0 40. 0 41. 0 42. 1 43. 1 44. 1 45. 4 46. 2 47. 1 48. Does not exist 49. 1 50. 1 51. - 1 52. 1 53. 2 54. Does not exist 55. Does not exist 56. 0 57. 0 58. 3 59. 2 60. 1 61. 1 - 1 - 1 - 2 - 3 - 4 - 5 - 2 - 3 - 4 - 5 2 3 4 5 5 4 3 2 1 x y f ( x ) = ƒ x ƒ 0, 2 62. f ( x ) = x 2 1 - 1 - 1 - 2 - 3 - 4 - 5 2 3 4 5 5 4 3 2 9 8 7 6 1 x y 1, 0 77. H 1 2 3 4 5 - 1 - 2 - 3 - 4 - 5 - 5 - 4 - 3 - 2 - 1 1 2 3 4 5 x y does not exist, 2 78. G 2 4 - 2 - 4 2 4 6 8 x y 1, 9 79. $3.50, $3.50, $3.50 80. $3.00, $3.50, does not exist 81. $4.00, $4.50, does not exist 82. $1.00, $1.21, does not exist 83. $1.21, $1.42, does not exist 84. $1.42, $1.42, $1.42 85. Does not exist 86. $1.63 87. 10%, 12%, does not exist 88. 12%, 12%, 12% 89. 22%, does not exist 90. 10%, 10%, 10% 91. 12%, 22%, does not exist 92. 22%, does not exist 93. 3 94. - 3 95. - 1 96. (a) 0; (b) 2; (c) answers may vary. 97. (a) 4; (b) 4, (c) 4; (d) 4; (e) 4; (f) no; (g) yes 98. Does not exist, 2 99. 0, 0 100. Does not exist, 1 6 63. g ( x ) = x 2 - 5 1 - 1 - 1 - 2 - 3 - 4 - 5 - 2 - 3 - 4 - 5 2 3 4 5 5 4 3 2 1 x y - 5, - 4 64. 1 - 1 - 1 - 2 - 3 - 4 - 2 - 3 - 4 - 5 2 3 4 5 5 4 6 3 2 1 x y g ( x ) = ƒ x ƒ + 1 4, 1 65. 1 - 1 - 5 - 4 - 3 - 2 - 1 - 2 - 3 - 4 - 5 - 6 - 7 2 3 5 4 3 2 1 x y G ( x ) = 4 x + 2 4, does not exist 66. 1 - 1 - 5 - 4 - 3 - 2 - 1 - 2 2 3 4 5 6 7 8 5 4 3 2 1 x y F ( x ) = 2 x - 3 does not exist, 2 67. 1 - 1 - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 2 - 3 - 4 - 5 2 3 4 5 3 2 1 x y f ( x ) = 1 - 2 x x - 2, does not exist 68. 1 - 1 - 1 - 2 - 2 - 3 - 4 - 5 2 3 4 5 5 4 6 7 8 3 2 1 x y f ( x ) = 1 + 3 x x 3, does not exist 71. 1 - 1 - 1 - 2 - 3 - 4 - 5 - 2 - 3 - 4 - 5 2 3 4 5 5 4 3 2 1 x F y 3, 1, does not exist 72. 1 - 1 - 1 - 2 - 2 - 3 2 3 4 5 6 7 5 4 7 8 6 3 2 1 x G y 1, 3, does not exist 73. 1 - 1 - 1 - 2 - 3 - 2 2 3 4 5 6 7 8 5 4 7 6 3 2 1 x y g 1, 0, does not exist 74. 1 2 3 4 5 - 1 - 2 - 3 - 4 - 5 - 5 - 4 - 3 - 2 - 1 1 2 3 4 5 x y f - 1, - 1, - 1 75. F 1 2 - 1 - 2 - 3 - 1 1 2 3 x y - 1 76. G 1 2 - 1 - 2 - 1 1 2 3 4 x y 1

83 more pages in the full document

Unlock it once and it stays in your library, ready to chat with or turn into flashcards.

Unlock the full document

More Mathematics study materials

See all

Study this document with CramX

Once it is in your library, every tool can work from it.