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

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Solution Manual for Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences, 14th Edition - Page 1 preview image

INSTRUCTORANSWERSFINITEMATHEMATICSFORBUSINESS,ECONOMICS,LIFESCIENCES,ANDSOCIALSCIENCESFOURTEENTHEDITIONRaymond BarnettMerritt CollegeMichael ZieglerMarquette UniversityKarl ByleenMarquette UniversityChristopher J. StockerMarquette University

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Solution Manual for Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences, 14th Edition - Page 2 preview image

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Solution Manual for Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences, 14th Edition - Page 3 preview image

Diagnostic Prerequisite TestSection references are provided in parentheses following each answerto guide students to the specific content in the book where they canfind help or remediation.1.(A) (y+z)x(B) (2+x)+y(C) 2x+3x(A.1)2.x3-3x2+4x+8(A.2)3.x3+3x2-2x+12(A.2)4.-3x5+2x3-24x2+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)7.14x2-30x(A.2)8.6x2-5xy-4y2(A.2)9.1x+221x+52(A.3)10.x1x+321x-52(A.3)11.7>20(A.1)12.0.875(A.1)13.(A) 4.065*1012(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 twoexamples of infinitely many.(A.1)17.6x5y15(A.5)18.3u4>v2(A.5)19.6*102(A.5)20.x6/y4(A.5)21.u7>3(A.6)22.3a2>b(A.6)23.59(A.5)24.x+2x1>2y1>2+y(A.6)25.a2+b2ab(A.4)26.a2-c2abc(A.4)27.y5x(A.4)28.1xy2(A.4)29.-17(7+h)(A.4)30.xyy-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)33.4x=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={17(A.7)39.x=-4, 5(A.7)40.x=1,16(A.7)A-1ANSWERS

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Solution Manual for Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences, 14th Edition - Page 4 preview image

(B)xint.: 6.5;yint.: 5.2(C)1021010210(D)xint.: 6.5;yint.: 5.2Chapter 1Exercises 1.11.x=52.x=-93.x=24.x=-35.x=-196.x=-27.4…x6138.-36x…59.-26x6710.-6…x… -111.x…412.xÚ913.1-8, 2414.3-1, 5215.1-∞, 9216.34,∞217.1-7,-5418.3-3,2219.x=-3220.m=1421.y6 -15222.x7 -10323.u=-3424.y=2325.x=1026.x=427.yÚ328.x…829.x=3630.y=-631.m636732.u61633.3…x67or33, 7237x34.-2…x63or3-2, 32223x35.-20…C…20or3-20, 20420x22036.-9…t…9or3-9, 949t2937.y=34x-338.x=-32y+1 239.y=-1A>B2x+1C>B2=1-Ax+C2 >B40.m=y-bx41.C=591F-32242.F=95C+3243.-26x…1or1-2,14122x44.143…u…6orc143 , 6d6u14345.Negative46.Positive47.4,500 $35tickets and 5,000 $55 tickets48.30 quarters; 70 dimes49.Fund A: $180,000;Fund B: $320,00050.Fund A: $340,000; Fund B: $160,00051.$15,40552.$24,49353.(A) $420(B) $5554.(A) $51(B) $16055.34 rounds56.12 times57.$32,00058.(A) $20,000(B) $24,493(C) Choose thepayment method with the larger base salary unless you can sell more than$52,000 per month.59.5,851 books60.7,132 books61.(B) 6,180 books(C) At least $11.5062.(B) 7,480 books(C) At least $15.6063.5,00064.-45…C… -1065.12.6 yr66.9.6 to 16.8Exercises 1.21.(D)2.(A)3.(C)4.(B)5.y55x6.y55x7.y36x8.y15x9.Slope=5;yint.=-710.Slope=3;yint.=211.Slope=-52;yint.=-912.Slope=-103 ;yint.=413.Slope=14;yint.=2314.Slope=15;yint.=-1215.Slope=2;xint.=-516.Slope=-4;xint.=317.Slope=8;xint.=518.Slope=-3;xint.=219.Slope=67;xint.=-720.Slope=-92;xint.=4921.y=2x+122.y=x+523.y=-13x+624.y=67x-9225.xint.: 12;yint.:1;y=-2x+126.xint.: 1;yint.: 3;y=-3x+327.xint.:-3;yint.:1;y=x3+128.xint.: 2; y int.:-1;y=x2-129.y55x30.y55x31.(D)xint.: 3.5;yint.:-4.2y55x32.y55x33.y55xy522x5334.y55xy52x52335.-436.537.-3538.2339.240.1841.(A)(B)(C)y1010x42.(A)(B)(C)y610x43.yx3,00010044.yx5,0004,0003,0002,0001,0001002006045.(A)y1010x(B)xint.: 3.5;yint.:-4.2(C)102101021046.(A)y106xANSWERSA-2

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Solution Manual for Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences, 14th Edition - Page 5 preview image

AnswersA-386.(A)p=0.0005x-1.7(B)p=-0.0005x+7.8(C) (9,500, 3.05)(D)px3.203.002.809,800SupplyDemand9,2000DollarsMillions of BushelsEquilibrium point47.x=4,y=-348.x=-5;y=649.x=-1.5,y=-3.550.x=2.6;y=3.851.y=5x-1552.y=4x+653.y=-2x+754.y=-10x+1555.y=13x-20356.y=27x-157.y=-3.2x+30.8658.y=0.9x+4.6359.(A)m=23(B)-2x+3y=11(C)y=23x+11360.(A)m=32(B) 3x-2y=-1(C)y=32x+1261.(A)m=-54(B)5x+4y=-14(C)y=-54x-7262.(A)m=-45(B) 4x+5y=23(C)y=-45x+23563.(A) Not defined(B)x=5(C) None65.(A)m=0(B)y=5(C)y=566.(A) Not defined(B)x=2(C) None67.The graphshave the sameyint., (0,2).68.The graphs have the same slope,-0.5.69.C=124+0.12x; 1,050 donuts70.C=1,200+45x;80 picnic tables71.(A)C=75x+1,647(B)Cx5,00010,00015,000005051001(C)Theyint., $1,647,is the fixed costand the slope,$75, is the costper club.72.(A)C=39x+1,905(B)Cx6,0004,0002,00010020060(C)The y int., $1,905,is the fixed cost,and the slope,$39, is the costper racket.73.(A)R=1.4C-7(B) $13774.(A)R=1.5C+3(B) $15875.(A)V=-7,500t+157,000(B) $112,000(C) During the 12th year(D)Vt$40,000$80,000$120,00010020Years(6, 112,000)(11.6, 70,000)76.(A)V=-6,800t+224,000(B) $156,000(C) During the 19th year(D)Vt$40,000$80,000$120,000$160,000$200,00010020Years(10, 156,000)(18.24, 100,000)77.(A)T=-1.84x+212(B) 205.56°F(C) 6,522 ft(D)Tx22018019020021020100Temperature (8F)Thousands of Feet(3.5, 205.56)(6.522, 200)78.(A)T=14x-206.6(B) 227.4°F(C) 28.97 inHg(D)Tx2252152051951853228300Temperature (8F)Barometric Pressure(inHg)(31, 227.4)(28.97, 199)79.(A)T=70-3.6A(B) 10,000 ft80.(A)T=3.2A+200(B) 220.8 mph81.(A)N=-0.0063t+2.76(B) 2.45 persons82.(A)I=1,031t+30,000(B) $71,24083.(A)f=-0.49t+21(B) 202884.(A)m=-0.6t+25.7(B) 203185.(A)p=0.001x+5.4(B)p=-0.001x+13(C) (3,800,9.2)(D)px109.594,2000004,3DollarsEquilibrium pointDemandSupply87.(A)s=25w(B) 8 in.(C) 9 lbExercises 1.31.(A)w=49+1.7h(B)The rate of change of weight with respect toheight is 1.7 kg/in.(C)55.8 kg(D)5′6.5″2.(A)w=52+1.9h(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=0.445d+14.7(B)The rate ofchange of pressure with respect to depth is 0.445lb/in.2per ft.(C)37 lb/in.2(D)99 ft4.(A)P=0.43d+14.7(B) The rate of change of pressurewith respect to depth is 0.43 lb/in.2 per ft.(C) 36.3 lb/in.2(D) 102 ft5.(A)a=2,880-24t(B)-24ft/sec(C)24 ft/sec6.(A)a=-16t+2,880(B)-16ft/sec(C) 16 ft/sec7.s=0.6t+331; the rate of change of the speed of sound with respectto temperature is 0.6 m/s per °C.8.x=3.9t+1,403;the rate of changeof the speed of sound with respect to temperature is 3.9 m/s per °C.9.(A)yx1008060402025 305010 15 20U.S. Fossil FuelProduction (%)Years since 1985(B)The rate of change of fossil fuelproduction is-0.19%per year.(C)76% of total production(D)205810.(A)yx1008060402025 305010 15 20U.S. Fossil FuelConsumption (%)Years since 1985(B)The rate of change of fossil fuelconsumption is-0.14% per year.(C) 81%(D) 203011.(A)ft25201510515 183069 12Female Smokers (%)Years since 199712.(A)mt25201510515 183069 12Male Smokers (%)Years since 199713.(A)yx10.510.50Licensed Drivers(millions)Population (millions)(B)1,050,000(C)1,359,000(B)2025(B) 202914.(A)yx402040200Licensed Drivers(millions)Population (millions)(B) 6,428,000(C) 10,339,00015.(A)St60030020100Net Sales (millions)Years since 2000(B)$662 billion88.(A)d=-4w+30(B) 30 in.(C) 7.5 lb

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Solution Manual for Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences, 14th Edition - Page 6 preview image

A-4Answers17.(A)yx2480302302600Ethylene Glycol(%wt)Degrees (8F)(B)2°F(C)22.75%18.(A)yx3060903030600Propylene 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 87,000students per year; undergraduate female enrollment is increasingat a rate of 140,000 students per year.(B) Male: 8.6 million;female: 11.5 million(C) 202622.(A) Graduate male enrollment isincreasing at a rate of 11,000 students per year; graduate female enrollmentis increasing at a rate of 31,000 students per year.(B) Male: 1.3 million;female: 2.1 million(C) 203723.y=0.061x+50.703; 54.67°F24.y=0.051x+30.166;33.48 in.25.Men:y=-0.070x+49.058;women:y=-0.085x+54.858; yes26.Men:y=-0.247x+119.097;Women:y=-0.122x+128.494; no27.Supply:y=0.2x+0.87;demand:y=-0.15x+3.5; equilibrium price=$2.3728.Supply:y=1.53x+2.85; demand:y=-2.21x+10.66; equilibrium price: $6.05Chapter 1 Review Exercises1.x=2.8(1.1)2.x=2(1.1)3.y=1.8-0.4x(1.1)4.x=43y+73(1.1)5.y6134ora-∞,134by134(1.1)6.1…x63 or [1, 3)13x(1.1)7.xÚ92orc92,∞b92x(1.1)8.y45x(1.2)9.2x+3y=12(1.2)10.xint.=9;yint.=-6; slope=23(1.2)y1010x11.y=-23x+6(1.2)16.(A)It402000102Operating Income(millions)Years since 2000(B) $37.2 billion21.xÚ1or[1,∞)(1.1)1x22.x6 -14317ora-∞,-14317b143172x(1.1)23.16x…4or(1, 4441x(1.1)24.38…x…78orc38,78dx7838(1.1)25.(A)(B)(C)y1010x(1.2)26.The graph ofx=-3 is a vert. line withxint.-3, and the graph ofy=2 is a hor.line withyint. 2.(1.2)yx5527.(A) An oblique line through the origin with slope-34(B) A vert. linewithxint.-43(C) Thexaxis(D) An oblique line withxint. 12 andyint.9(1.2)28.2A-bhh(1.1)29.S-PSt(1.1)30.a60andbany realnumber(1.1)31.Less than(1.1)32.The graphs appear to be perpendicularto each other. (It can be shown that if the slopes of two slant lines are thenegative 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=132-0.6x(B)M=187-0.85x(C) Between 120 and 170 beats per minute(D) Between 102 and 144.5 beats per minute(1.3)36.(A)V=224,000-15,500t(B) $38,000(1.2)37.(A)R=1.6C(B) $192(C) $110(D) The slopeis 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=5.24-0.00125x; 1,560 bottles(1.2)40.(A)TM401208040048 6012(B)-30°F(C) 45%(1.3)41.(A) The dropout rate is decreasing at a rate of 0.308 percentage pointsper year.(B)rt201000204Dropout 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=-23x(B)y=3(1.2)14.(A) 3x+2y=1(B)y=5(C)x=-2(1.2)15.x=252(1.1)16.u=36(1.1)17.x=3011(1.1)18.x=21(1.1)19.x=4(1.1)20.x64or1-∞,42(1.1)4x

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Solution Manual for Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences, 14th Edition - Page 7 preview image

Chapter 2Exercises 2.11.yx552.yx553.yx5104.yx1055.yx5056.yx5507.yx438.yx10109.A function10.A function11.Not a function12.Not a function13.A function14.A function15.A function16.A function17.Not a function18.Not a function19.A function20.Not a function21.Linear22.Neither23.Neither24.Linear25.Linear26.Neither27.Constant28.Constant29.yx5530.yx5331.yx10532.yx10533.yx50534.yx50535.yx101036.yx4437.yx5538.y55x39.y=040.y=041.y=442.y=343.x=-544.x=545.x=-646.x=-5,0, 447.All real numbers48.All real numbers49.All real numbers except-450.All real numbersexcept 251.x…752.x7 -553.Yes; all realnumbers54.Yes; all real numbers55.No; for example, whenx=0,y={256.Yes; all real numbers except 057.Yes; all real numbers except 058.No; whenx=0,y={359.No;whenx=1,y={160.Yes;xÚ061.25x2-462.9x2-463.x2+4x64.x2-2x-365.x4-466.x6-467.x-468.1x-469.h2-470.h2+171.4h+h272.5-6h+h273.4h+h274.-6h+h275.(A)4x+4h-3(B)4h(C)476.(A)-3x-3h+9(B)-3h(C)-377.(A)4x2+8xh+4h2-7x-7h+6(B)8xh+4h2-7h(C)8x+4h-778.(A) 3x2+6xh+3h2+5x+5h-8(B) 6xh+3h2+5h(C) 6x+3h+579.(A)20x+20h-x2-2xh-h2(B)20h-2xh-h2(C)20-2x-h80.(A)x2+2xh+h2+40x+40h(B) 2xh+h2+40h(C) 2x+h+4081.P1w2=2w+50w,w7082.P1l2=2l+162l,l7083.A1l2=l150-l2,06l65084.A1w2=180-w2w, 06w68086.(A)px$2,00025(B)$54; $42(B) $1,340; $92087.(A)R1x2=175-3x2x,1…x…20(B)xR(x)17242528408124681643220300(C)R(x)x$5002088.(A)R1x2=x12,000-60x2, 1…x…25(B)xR(x)11,94058,5001014,0001516,5002016,0002512,500(C)R(x)x$15,0002589.(A)P1x2=59x-3x2-125,1…x…20(B)xP(x)1-69463815512151165120-145(C)P(x)$2002200x1590.(A)P1x2=1,500x-60x2-4,000,1…x…25(B)xP(x)1-2,56052,000105,000155,000202,00025-4,000(C)P(x)x25$5,00091.v=75-w15+w; 1.9032 cm/sec92.(A)v=0.4s+0.28; 48.4%(B)s=2.5v-0.7;57.5%ANSWERS85.(A)p(x)x$10020Exercises 2.21.Domain: all real numbers; range: [-4,∞]2.Domain:30,∞2; range:31,∞23.Domain: all real numbers; range: all real numbers4.Domain: all realnumbers; range:310,∞25.Domain: [0,∞2; range:1-∞,8]6.Domain:all real numbers; range: all real numbers7.Domain: all real numbers; range:all real numbers8.Domain: all real numbers; range:1-∞, 15]9.Domain: allreal numbers; range: [9,∞210.Domain: all real numbers; range: all realnumbers11.x5512.x5513.x55A-5

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Solution Manual for Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences, 14th Edition - Page 8 preview image

A-6Answers28.The graph ofh1x2=-0x-50is the graph ofy=0x0reflected in thexaxis and shifted 5 units to the right.h(x)x101029.The graph off1x2=1x-422-3 is the graph ofy=x2shifted 4 unitsto the right and 3 units down.f(x)x101030.The graph ofm1x2=1x+322+4 is the graph ofy=x2shifted3 units to the left and 4 units up.x1010m(x)31.The graph off1x2=7-1xis the graph ofy=1xreflected in thexaxis and shifted 7 units up.f(x)x101032.The graph ofg1x2=-6+13xis the graph ofy=13xshifted 6 unitsdown.x1010g(x)44.g1x2=13x+3+2g(x)x5545.g1x2=-x+3g(x)x5546.g1x2=-0x-10g(x)x5547.g1x2=-1x-223-1g(x)x5548.g1x2=4-1x+222g(x)x5549.f(x)x5550.g(x)x5551.h(x)x302052.h(x)x604053.h(x)x1008054.h(x)x30020055.The graph of thebasic functiony=xis reflected in thexaxisand vertically shrunk bya factor of 0.5. Equation:y=-0.5x.14.x5515.x5216.x5517.x5518.x5519.x5520.x5521.x5522.x5523.x5524.x5525.x5526.x5527.The graph ofg1x2=-x+3is thegraph ofy=xreflectedin thexaxis and shifted3 units to the left.g(x)x101033.The graph ofh1x2=-3xis the graph ofy=xreflected in thexaxis and vertically stretched by a factor of 3.h(x)x101034.The graph ofm1x2=-0.4x2is the graph ofy=x2reflected in thexaxis and vertically shrunk by a factor of 0.4.x1010m(x)35.The graph of the basic functiony=x2is shifted 2 units to the left and3 units down. Equation:y=1x+222-3.36.The graph of the basicfunctiony=0x0is shifted 3 units to the right and 2 units up. Equation:y=0x-30+2.37.The graph of the basic functiony=x2is reflectedin thexaxis and shifted 3 units to the right and 2 units up. Equation:y=2-1x-322.38.The graph of the basic functiony=0x0isreflected in thexaxis, shifted 2 units to the left and 3 units up. Equation:y=3-0x+20.39.The graph of the basic functiony=1xis reflectedin thexaxis and shifted 4 units up. Equation:y=4-1x.40.The graphof the basic function13xis reflected in thexaxis and shifted 2 units up.Equation:y=2-13x.41.The graph of the basic functiony=x3isshifted 2 units to the left and 1 unit down. Equation:y=1x+223-1.42.The graph of the basic functiony=x3is reflected in thexaxis, shifted 3units to the right and 1 unit up. Equation:y=1-1x-323.43.g1x2=1x-2-3g(x)x55

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Solution Manual for Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences, 14th Edition - Page 9 preview image

AnswersA-756.The graph of the basic functiony=xis reflected in thexaxis andvertically stretched by a factor of 2. Equation:y=-2x.57.The graph ofthe basic functiony=x2is reflected in thexaxis and vertically stretchedby a factor of 2. Equation:y=-2x2.58.The graph of the basic functiony=0x0is vertically stretched by a factor of 4. Equation:y=40x0.59.The graph of the basic functiony=23xis reflected in thexaxis andvertically stretched by a factor of 3. Equation:y=-323x.60.The graphof the basic functiony=x3is vertically shrunk by a factor of 0.25. Equation:y=0.25x3.61.Reversing the order does not change the result.62.Reversing the order does not change the result.63.Reversing the ordercan change the result.64.Reversing the order can change the result.65.Reversing theorder can change the result.66.Reversing the order does notchange the result.67.(A)The graph of the basic functiony=1xis reflectedin thexaxis, vertically expanded by a factor of 4, and shifted up 115 units.(B)p(x)x$100$50100020068.(A) The graph of the basic functiony=1xis vertically expanded by a factor of 4.(B)p(x)x10050200100069.(A)The graphof the basic functiony=x3is verticallycontracted by a factorof 0.000 48 and shiftedright 500 units and up60,000 units.(B)C(x)x$100,000$50,0005000100070.(A) The graph of the basic functiony=x2is reflected in thexaxis, vertically contractedby a factor of 0.013, and shifted 10 units to theright and 190 units up.(B)p(x)x2505010015020010050071.(A)S1x2=e8.5+0.065xif 0…x…700-9+0.09xifx7700(B)S(x)x1001,40072.(A)W1x2=e8.5+0.065xif0…x…70016.9+0.053xifx7700f(B)Wx100130073.(A)T1x2=•0.02xif 06x…25,0000.04x-500if 25,0006x…100,0000.06x-2,500ifx7100,000(B)T(x)x3,000100,000(C)$1,700; $4,10074.(A)T1x2=•0.02xif 0…x612,5000.04x-250if 12,5006x…50,0000.06x-1,250ifx750,000(B)T(x)x1,50050,000(C) $1,030; $2,59075.(A)The graph of thebasicfunctiony=xis vertically stretched bya factor of 5.5 and shifted down 220 units.(B)w(x)x2002505010015050010076.(A) The graph of the basic functiony=x3is vertically stretched by afactor of 463.(B)w(x)x2505010015020010.5077.(A)The graph of the basic functiony=1xis vertically stretched by afactor of 7.08.(B)v(x)x1005050010078.(A) The graph of the basic functiony=13xis reflected in thexaxis andshifted up 10 units.(B)T(x)x10512525 50 750Exercises 2.31.f1x2=1x-522-252.f1x2=1x+822-643.f1x2=1x+1022-504.f1x2=1x-622-445.f1x2=-21x-122-36.f1x2=31x+322-67.f1x2=2ax+12b2+128.f1x2=-5ax-32b2+149.The graph off1x2is the graph ofy=x2shifted right 2 units and down1 unit.10.The graph ofg1x2is the graph ofy=x2shifted right 1 unit anddown 6 units.11.The graph ofm1x2is the graph ofy=x2reflected in thexaxis, then shifted right 3 units and up 5 units.12.The graph ofn1x2isthe graph ofy=x2reflected in thexaxis, then shifted right 4 units and up7 units.13.(A)m(B)g(C)f(D)n14.(A)g(B)m(C)n(D)f15.(A)xint.: 1, 3;yint.:-3(B)Vertex: (2, 1)(C)Max.: 1(D)Range:y…1 or1-∞, 1416.(A)xint.:-5,-1;yint.:-5(B) Vertex:1-3, 42(C) max.: 4(D) Range:y…4 or1-∞, 4417.(A)xint.:-3,-1;yint.: 3(B)Vertex:1-2,-12(C)Min.:-1(D)Range:yÚ -1 or3-1,∞218.(A)xint.: 1, 5;yint.: 5(B) Vertex:13,-42(C) min.:-4(D) Range:yÚ -4 or3-4,∞219.(A)xint.: 3{12;yint.:-7(B)Vertex:13, 22(C)Max.: 2(D)Range:y…2 or1-∞, 2420.(A)xint.:-2{13;yint.:-1(B) Vertex:1-2, 32(C) max.: 3(D) Range:y…3 or1-∞, 3421.(A)xint.:-1{12;yint.:-1(B)Vertex:1-1,-22(C)Min.:-2(D)Range:yÚ -2 or3-2,∞222.(A)xint.: 4{13;yint.: 13(B) Vertex:14,-32(C) min.:-3(D) Range:yÚ -3 or3-3,∞223.y=-3x-1-2242+5ory=-1x+222+524.y=-1x-422+225.y=1x-122-326.y=3x-1-3242+1ory=1x+322+127.Vertex form:1x-422-4(A)xint.: 2, 6;

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Solution Manual for Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences, 14th Edition - Page 10 preview image

A-8Answersyint.: 12(B)Vertex:14,-42(C)Min.:-4(D)Range:yÚ -4or3-4,∞228.Vertex form:1x-322-4(A)xint.: 1, 5;yint.: 5(B) Vertex:13,-42(C) min.:-4(D) Range:yÚ -4or3-4,∞229.Vertex form:-41x-222+1(A)xint.: 1.5, 2.5;yint.:-15(B)Vertex:12, 12(C)Max.: 1(D)Range:y…1 or1-∞, 1430.Vertex form:-41x+122+1(A)xint.:-32,-12;yint.:-3(B) Vertex:1-1, 12(C) max.: 1(D) Range:y…1 or1-∞, 1431.Vertex form: 0.51x-222+3(A)xint.: none;yint.: 5(B)Vertex:12, 32(C)Min.: 3(D)Range:yÚ3 or33,∞232.Vertex form: 0.51x+422+2(A)xint.: none;yint.: 10(B) Vertex:1-4, 22(C) min.: 2(D) Range:yÚ2 or32,∞233.(A)-4.87, 8.21(B)-3.44, 6.78(C)No solution34.(A)-1.53, 6.53(B) 0.36, 4.64(C) No solution35.651.041736.347.142937.g1x2=0.251x-322-9.25(A)xint.:-3.08,9.08;yint.:-7(B)Vertex:13,-9.252(C)Min.:-9.25(D)Range:yÚ -9.25 or3-9.25,∞238.m1x2=0.201x-422-4.2(A)xint.:-0.58, 8.58;yint.:-1(B) Vertex:14,-4.22(C) min.:-4.2(D) Range:yÚ -4.2 or3-4.2,∞239.f1x2=-0.121x-422+3.12(A)xint.:-1.1, 9.1;yint.: 1.2(B)Vertex:14, 3.122(C)Max.: 3.12(D)Range:y…3.12 or1-∞, 3.12440.n1x2=-0.151x+322+4.65(A)xint.:-8.57, 2.57;yint.: 3.30(B) Vertex:1-3, 4.652(C) max.: 4.65(D) Range:y…4.65 or1-∞, 4.65441.1-∞,-52h13,∞242.1-6, 3243.3-3, 2444.1-∞,-44∪3-3,∞245.x=-5.37, 0.3746.x=-1.27, 2.7747.-1.376x62.1648.-0.88…x…3.5249.x… -0.74 orxÚ4.1950.x6 -1orx72.7251.Axis:x=2; vertex: (2, 4); range:yÚ4 or34,∞2; noxint.52.Axis:x=-3; vertex:1-3,-52; range:y… -5 or1-∞,-5]; noxintercept53.(A)yxgf1510(B)1.64, 7.61(C)1.646x67.61(D)0…x61.64 or 7.616x…1054.(A)yxgf107(B) 0.93, 5.35(C) 0.936x65.35(D) 0…x60.93 or 5.356x…755.(A)yx1510gf(B)1.10, 5.57(C)1.106x65.57(D)0…x61.10 or 5.576x…856.(A)yxgf1510(B) 1.08, 6.35(C) 1.086x66.35(D) 0…x61.08 or 6.356x…965.(A)x2830323436Mileage4552555147f(x)45.351.854.252.446.5(B)yx50403020103628032(C)f1312=53.50 thousand miles;(D)f1352=49.95 thousand miles;69.(A)R(x)x50020(B)12.5 (12,500,000 chips);$468,750,000(C)$37.5070.(A)Rx16,00025(B) 16.667 (16,667 computers);$16,667,000(C) $1,00071.(A)yx50020CR(B)2,415,000 chips and 17,251,000chips(C)Loss: 1…x62.415or 17.2516x…20; profit:2.4156x617.25172.(A)yRCx16,00025(B) 3,035 computers and 21,965computers(C) Loss: 1…x63.035or 21.9656x…25; profit:3.0356x621.96573.(A)P1x2=59x-3x2-125CRPyx500220015(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)P1x2=1,500x-60x2-4,000yRPCx16,00025(C) Intercepts and break-evenpoints: 3,035 computers and21,965 computers(D) Maximum profit is$5,375,000 at a production levelof 12,500 computers. This ismuch smaller than the maximumrevenue of $16,666,667.75.x=0.14 cm76.x=0.10 cm77.10.6 mph78.5.6 mpg66.(A)x5101520253035Market share18.820.020.720.217.416.415.3f(x)19.219.920.119.618.617.014.8(B)yx2035(C)f1452=8.6%;f1482=6.3%

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Solution Manual for Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences, 14th Edition - Page 11 preview image

AnswersA-9Exercises 2.41.(A) 1(B)-3(C) 212.(A) 2(B) 2, 3(C) 63.(A) 2(B)-5,-4(C) 204.(A) 1(B) 10(C) 305.(A) 6(B) None(C) 156.(A) 8(B) None(C) 107.(A) 5(B) 0,-6(C) 08.(A) 4(B)-7, 5(C) 1,2259.(A) 11(B)-5,-2, 5(C)-12,80010.(A) 10(B)-3, 52, 3(C) 164,02511.(A)4(B)Negative12.(A) 2(B) Negative13.(A)5(B)Negative14.(A) 3(B) Negative15.(A)1(B)Negative16.(A) 4(B) Positive17.(A)6(B)Positive18.(A) 6(B) Positive19.1020.721.122.023.(A)xint.:-2;yint.:-1(B)Domain: all realnumbers except 2(C)Vertical asymptote:x=2; horizontal asymptote:y=1(D)f(x)x101024.(A)xint.: 3;yint.:-1(B) Domain: all realnumbers except-3(C) Vertical asymptote:x=-3;horizontal asymptote:y=1(D)f(x)1010x25.(A)xint.: 0;yint.: 0(B)Domain: all realnumbers except-2(C)Vertical asymptote:x=-2;horizontal asymptote:y=3(D)f(x)x101026.(A)xint.: 0;yint.: 0(B) Domain: all real numbers except 3(C) Verticalasymptote:x=3; horizontal asymptote:y=2(D)f(x)1010x27.(A)xint.: 2;yint.:-1(B)Domain: all real numbers except 4(C)Vertical asymptote:x=4; horizontal asymptote:y=-2(D)f(x)x101028.(A)xint.: 1;yint.:-32(B) Domain: all realnumbers except 2(C) Vertical asymptote:x=2;horizontal asymptote:y=-3(D)f(x)1010x29.(A)(B)30.(A)(B)31.(A)(B)32.(A)(B)33.y=5634.y=3235.y=1436.y=-1237.y=038.y=039.None40.None41.x=-1,x=1,x=-3,x=342.x=-2,x=2,x=-4,x=443.x=544.x=-845.x=-6,x=646.x=0,x=247.(A)xint.: 0;yint.: 0(B)Vertical asymptotes:x=-2,x=3; horizontal asymptote:y=2(C)f(x)x1010(D)48.(A)xint.: 0;yint.: 0(B) Vertical asymptotes:x=-3,x=2; horizontalasymptote:y=3(C)f(x)810x(D)49.(A)xint.:{13;yint.:-23(B)Vertical asymptotes:x=-3,x=3;horizontal asymptote:y=-2(C)f(x)x1010

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Solution Manual for Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences, 14th Edition - Page 12 preview image

A-10Answers(D)102101021050.(A)xint.:{1;yint.:-34(B) Vertical asymptote:x=-2,x=2;horizontal asymptote:y=-3(C)f(x)1010x(D)102101021051.(A)xint.: 6;yint.:-4(B)Vertical asymptotes:x=-3,x=2; horizontalasymptote:y=0(C)f(x)x1010(D)102101021052.(A)xint.: 2;yint.: 56(B) Vertical asymptotes:x=-4,x=3;horizontal asymptote:y=0(C)f(x)1010x(D)102101021053.f1x2=x2-x-254.f1x2=2-x-x255.f1x2=4x-x356.f1x2=x3-x57.(A)C1x2=180x+200(B)C1x2=180x+200x58.(A)C1x2=240x+300(B)C1x2=240x+300x(C)C(x)x60030(D) $240 per board59.(A)C1n2=2,500+175n+25n2n(B)n1,500200C(n)(C)10 yr; $675.00 per year(D)10 yr; $675.00 per year60.(A)C1x2=x2+2x+2,000x(B)x150C(x)500(C) 45 units; $91.44 per player(D) 45 units; $91.44 per player61.(A)C1x2=0.000481x-50023+60,000x(B)(C)750 cases per month;$90 per case62.(A)C1x2=20x3-360x2+2,300x-1,000x(B)(C) 8.667 thousand cases per month; $567per case63.(A)(B)1.7 lb64.(A)(B) 583 eggs65.(A)0.06 cm/sec(B)v(x)x510066.(A) 55 words per minute(B)x30f(x)6067.(A)(B)5.568.(A)(B) 2.5(C)x500300C(x)(D)$180 per board

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Solution Manual for Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences, 14th Edition - Page 13 preview image

AnswersA-11Exercises 2.51.(A)k(B)g(C)h(D)f2.(A)g(B)f(C)h(D)k3.yx304244.y304x5.yx304246.y304x7.f(x)x2304248.g2304x9.yx22042410.y2204x11.The graph ofgis the graph offreflected in thexaxis.12.Thegraph ofgis the graph offshifted2 units to the right.13.Thegraph ofgis the graph offshifted1 unit to the left.14.The graph ofgis the graph offreflected in thexaxis.15.The graphofgis the graph offshifted 1 unit up.16.The graph ofgis the graph offshifted 2 units down.17.The graph ofgis the graph offvertically stretchedby a factor of 2 and shifted to the left 2 units.18.The graph ofgis the graphoffvertically shrunk by a factor of 0.5 and shifted 1 unit to the right.19.(A)yx55(B)yx55(C)yx55(D)yx5420.(A)yx55(B)yx55(C)yx55(D)yx5521.f(t)t103023022.G(t)10250t23.yx2021052524.y205x25.yx2042426.y14x27.a=1,-128.a=2,b=-2,for example29.x=4830.x=931.x=-2, 532.x=-6, 733.x=-934.x=1635.x=3, 1936.x=0, 237.x=-4,-338.x=1, 1139.x=-740.x=1>241.x=-2,242.x=-3, 343.x=1>444.No solution45.No solution46.x=2>347.h(x)x20.52548.yx0.5449.Nt100550.Nt200551.$16,064.0752.$32,542.7253.(A)$2,633.56(B)$7,079.5454.(A) $4,121.75(B) $7,285.9555.$10,70656.$15,70557.(A)$10,095.41(B)$10,080.32(C)$10,085.2758.(A) $10,697.09(B) $10,671.21(C) $10,644.9359.Napproaches 2 astincreases without bound.Nt25060.40 boards per dayNt403062.(A)61.(A)(B)9.94 billion(B) 268.8 exabytes per month63.(A)10%(B)1%64.(A) 62%(B) 39%65.(A)P=12e0.0402x(B)17.9 million66.(A)P=204e0.0077x(B) 229 million67.(A)P=127e-0.0016x(B)124 million68.(A)P=7.4e0.0113x(B) 2025: 8.2 billion; 2033: 9.0 billionExercises 2.61.27=332.32=253.100=14.e0=15.8=43>26.27=93>27.log749=28.log636=29.log48=3210.log279=2>311.logbA=u12.logbM=x13.614.-315.-516.417.718.-619.-320.Not defined21.Not defined22.-123.logbP-logbQ24.logbF+logbG25.5 logbL26.15 logbw27.qp28.logRP29.x=1>1030.x=1031.b=432.b=1>533.y=-334.y=1>235.b=1>336.b=10037.x=838.x=3239.False40.False41.True53.No solution54.x=455.yx51056.y58x57.The graph ofy=log21x-22is the graph ofy=log2xshifted tothe right 2 units.59.Domain:1-1,∞2; range: all real numbers60.Domain:11,∞2; range:all real numbers61.(A)3.547 43(B)-2.160 32(C)5.626 29(D)-3.197 0462.(A) 1.860 96(B)-1.48095(C) 10.603 04(D)-5.1283663.(A)13.4431(B)0.0089(C)16.0595(D)0.151464.(A) 121.1156(B) 0.0089(C) 22.9565(D) 0.013265.1.079266.2.184767.1.459568.-1.184569.18.355970.8.750771.Increasing:10,∞2yx3572.Decreasing:10,∞2y3x542.False43.True44.False45.False46.True47.x=248.x=1249.x=850.x=251.x=752.x=4

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Solution Manual for Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences, 14th Edition - Page 14 preview image

A-12Answers73.Decreasing:10, 14Increasing:31,∞2yx5574.Decreasing:1-∞, 02Increasing:10,∞2y35x75.Increasing:1-2,∞2yx5576.Increasing:10,∞2y6x577.Increasing:10,∞2y1010x78.Increasing:13,∞2y10x1079.Becauseb0=1 for any permissible baseb1b70,b12.80.Because the functiony=1xis not one-to-one81.x71x7lnxfor16x…1682.logx613x6x83.4 yr84.8 yr85.9.87 yr; 9.80 yr86.5.17 yr; 5.09 yr87.7.51 yr88.29.84 yr89.(A)5,37390.Equilibrium price: $46.77; Equilibrium quantity: 6,14592.(A) 30(B) 65(C) 80(D) 15093.168 bushels/acre(B)7,22094.12,628 million bushels95.912 yr96.18,569 yr21.(A)xintercepts:-4, 0;yintercept: 0(B)Vertex:1-2,-42(C)Min-imum:-4(D)Range:yÚ -4or3-4,∞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=0,32(2.5)31.x=-2(2.6)32.x=12(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 exceptx=-2and 3(B)x65(2.1)43.Vertex form:4ax+12b2-4;xintercepts:-32and12;yintercept:-3; vertex:1-12,-42; minimum:-4; range:yÚ -4or3-4,∞2(2.3)44.1-1.54,-0.792;10.69, 0.992(2.5, 2.6)45.yx505(2.1)46.yx105(2.1)47.6(2.1)48.-19(2.1)49.10x-4(2.1)50.21-5x(2.1)51.(A)-1(B)-1-2h(C)-2h(D)-2(2.1)52.(A)a2-3a+1(B)a2+2ah+h2-3a-3h+1(C)2ah+h2-3h(D)2a+h-3(2.1)53.The graph of functionmis the graph ofy=xreflected in thexaxis and shifted to the right 4 units.(2.2)54.The graph offunctiongis the graph ofy=x3vertically contracted by a factor of 0.3 andshifted up 3 units.(2.2)55.The graph ofy=x2is vertically expanded bya factor of 2, reflected in thexaxis, and shifted to the left 3 units. Equation:y=-21x+322.(2.2)56.f1x2=22x+3-1(2.2)x55f(x)57.y=0(2.4)58.y=34(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.yx1540(2.2)69.yx8050(2.2)Chapter 2 Review Exercises1.yx105(2.1)2.yx55(2.1)3.x55y(2.1)4.(A)Not a function(B)A function(C)A function(D)Not afunction(2.1)5.(A)-2(B)-8(C)0(D)Not defined(2.1)6.v=lnu(2.6)7.y=logx(2.6)8.M=eN(2.6)9.u=10v(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=-5or 5(2.1)18.(A)x55y(B)x55y(C)x55y(D)x55y(2.2)19.f1x2=-1x-222+4. The graph off1x2is the graph ofy=x2reflected inthexaxis, then shifted right 2 units and up4 units.(2.2)20.(A)g(B)m(C)n(D)f(2.2, 2.3)70.y=-1x-422+3(2.2, 2.3)71.f1x2=-0.41x-422+7.6(A)xintercepts:-0.4, 8.4;yintercept: 1.2(B)Vertex:14.0, 7.62(C)Maximum: 7.6(D)Range:y…7.6or1-∞, 7.64(2.3)72.(A)xintercepts:-.4, 8.4;yinter-cept: 1.2(B)Vertex: (4.0,7.6)(C)Maximum:7.6(D)Range:y…7.6or1-∞, 7.6](2.3)73.log 10p=pand10log12=12; lnep=pandeln12=12(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-5t(2.6)79.Iflog1x=y, then1y=x; that is,1=xforall positive real numbersx, which is not possible.(2.6)80.The graph ofy=23xis vertically expanded by a factor of 2, reflected in thexaxis, andshifted 1 unit left and 1 unit down. Equation:y=-223x+1-1.(2.2)81.G1x2=0.31x+222-8.1(A)xintercepts:-7.2, 3.2;yintercept:-6.9(B) Vertex:1-2,-8.12(C) Minimum:-8.1(D) Range:yÚ -8.1or3-8.1,∞2(2.3)

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Solution Manual for Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences, 14th Edition - Page 15 preview image

AnswersA-1382.(A)xintercepts:-7.2. 3.2;yintercept:-6.9(B) Vertex:1-2,-8.12(C) Minimum:-8.1(D) Range:yÚ -8.1 or [-8.1,∞2(2.3)83.(A)S1x2=μ3if 0…x…200.057x+1.86if 206x…2000.0346x+6.34if 2006x…1,0000.0217x+19.24ifx71,000(B)S(x)x501,500(2.2)84.$5,321.95(2.5)85.$5,269.51(2.5)86.201 months1≈16.7 years2(2.5)87.9.38 yr(2.5)88.(A)R(x)C(x)x60040CR(B)R=Cforx=4.686 thou-sand units (4,686 units) and forx=27.314 thousand units (27,314units);R6Cfor 1…x64.686or 27.3146x…40;R7Cfor4.6866x627.314.(C) Maxi-mum revenue is 500 thousand dollars($500,000). This occurs at an outputof 20 thousand units (20,000 units).At this output, the wholesale price isp1202=$25.(2.3)89.(A)P1x2=R1x2-C1x2=x150-1.25x2-1160+10x2(B)P=0 forx=4.686 thou-sand units (4,686 units) and forx=27.314 thousand units (27,314units);P60 for 1…x64.686or 27.3146x…40;p70 for4.6866x627.314.(C) Maximumprofit is 160 thousand dollars ($160,000).This occurs at an output of 16 thousandunits (16,000 units). At this output, thewholesale price isp1162=$30.(2.3)90.(A)A1x2=-32x2+420x(B) Domain: 0…x…280(C)A(x)x30,000300(D)There are two solutions to the equationA1x2=25,000, one near 90 and anothernear 190.(E) 86 ft; 194 ft(F) Maximumcombined area is 29,400 ft2. This occurs forx=140 ft andy=105 ft.(2.3)91.(A) 2,833 sets(B) 4,836(C)Equilibrium price: $131.59; equi-librium quantity: 3,587 cookwaresets(2.3)92.(A)(B) 4976(2.4)93.(A)N=22torN=4t(B)15 days(2.5)94.k=0.00942; 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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Solution Manual for Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences, 14th Edition - Page 16 preview image

Chapter 3Exercises 3.11.$25.422.$1,461.323.64%4.45.Slope=120;yint.=12,0006.Slope=300;yint.=15,0007.Slope=50;yint.=2,0008.Slope=175;yint.=5,0009.0.06210.8.5%11.13.7%12.0.043513.0.002514.0.19%15.0.84%16.0.003617.12yr18.34yr19.13yr20.14yr21.54yr22.326yr23.1013yr24.74yr25.$4226.$85.5027.$1,80028.$25029.0.12 or 12%30.0.16or 16%31.12yr32.34yr33.$4,612.5034.$3,011.2535.$87536.$5,60037.0.36 or 36%38.0.22 or 22%39.1 yr40.14yr41.r=I> 1Pt242.P=Irt43.P=A> 11+rt244.r=A-PPt45.t=A-PPr46.t=IPr47.The graphs are linear, all withyintercept$1,000; their slopes are 40, 80, and 120, respectively.48.The graphs are linear,withyintercepts 400, 800, and 1,200 and slopes 30, 60, and 90, respectively.49.$4550.$232.5051.$3052.$41.6753.$7,647.2054.$10,325.0055.8.1%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.$992.3864.$976.0765.$24.3166.$20.0067.$2768.$27.8269.5.396%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.$118.9480.$22.4181.$1,445.8982.$1,953.6083.$7.2784.$17.5985.$824.8586.$648.1087.630%88.429%89.771%90.431%Exercises 3.21.P=9502.P=2,5003.x=174.x=3.55.i=0.56.i=0.47.n=48.n=59.$5,983.4010.$3,008.7111.$4,245.0712.$11,352.5313.$3,125.7914.$1,544.9415.$2,958.1116.$12,935.0317.2.5 yr18.3.25 yr19.6.79%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; $27.0538.(A) $2,805.10; $805.10(B) $2,829.56; $829.56(C) $2,835.25; $835.2539.(A) $5,524.71(B) $6,104.4840.(A) $24,419.93(B) $27,527.9041.$12,175.6942.$174,250.5543.All three graphsare increasing, curve upward, and have the sameyintercept; the greater theinterest 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 areincreasing and curve upward; they haveyintercepts 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.PeriodInterestAmount0$1,000.001$97.50$1,097.502$107.01$1,204.513$117.44$1,321.954$128.89$1,450.845$141.46$1,592.296$155.25$1,747.5446.PeriodInterestAmount0$2,000.001$165.00$2,165.002$178.61$2,343.613$193.35$2,536.964$209.30$2,746.265$226.57$2,972.8347.(A) $7,440.94(B) $5,536.7648.(A) $4,730.96(B) $3,730.3349.(A) $19,084.49(B) $11,121.4550.(A) $2,970.16(B) $2,072.2151.(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%55.1123yr56.5.75 yr57.3.75 yr58.8.5 yr59.n≈1260.n≈1561.(A) 714yr(B) 6 yr62.(A) 9 yr(B) 10.5 yr63.(A) 7.7 yr(B) 6.3 yr64.(A) 3.3 yr(B) 2.1 yr65.$65,068.4466.$16,961.6667.$282,222.4468.$20,683.1069.$19.78 per ft2per mo70.$173,391.5071.(A) In 2026,250 years after the signing, it would be worth $175,814.55.(B) If interestwere 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 mo76.17 quarters or 4.25 yr77.$163,295.2178.$180,370,243.40; $20.2079.3,615 days; 8.453 yr80.8,021 days; 18.310 yr81.YearsExact RateRule of 72612.212.0710.410.389.19.098.08.0107.27.2116.56.5125.96.082.83.14 quarters84.17 months85.To maximize earnings, choose 10%simple interest for investments lastingfewer than 11 years and 7% compoundinterest otherwise.86.To maximize earnings, choose 9% simple interest for investments lastingfewer than 154 months and 6% compounded monthly otherwise.87.3.33%88.2.91%89.7.02%90.5.99%91.$15,843.8092.$13,261.8193.4.53%94.4.56%95.13.44%96.17.61%97.17.62%98.20.30%Exercises 3.31.1,0232.488,2813.3,0004.255.71,744,5306.444,4447.i=0.02;n=808.i=0.005;n=729.i=0.0375;n=2410.i=0.0625;n=1511.i=0.0075;n=4812.i=0.0425;n=1413.i=0.0595;n=1214.i=0.019;n=7215.FV=$13,435.1916.FV=$4,164.5917.PMT=$310.6218.PMT=$172.5719.n=1720.n=1321.i=0.0922.i=0.07ANSWERSA-14

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Solution Manual for Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences, 14th Edition - Page 17 preview image

AnswersA-1525.n=lna1+iFVPMTbln11+i226.i=FVPMT-227.Value: $84,895.40;interest: $24,895.4028.Value=$323,943.07; interest=$143,943.0729.$20,931.0130.$343,214.7331.$667.4332.$626.9333.$763.3934.$2,363.0735.PeriodAmountInterestBalance1$1,000.00$0.00$1,000.002$1,000.00$83.20$2,083.203$1,000.00$173.32$3,256.524$1,000.00$270.94$4,527.465$1,000.00$376.69$5,904.1536.PeriodAmountInterestBalance1$2,000.00$0.00$2,000.002$2,000.00$39.50$4,039.503$2,000.00$79.78$6,119.284$2,000.00$120.86$8,240.145$2,000.00$162.74$10,402.886$2,000.00$205.46$12,608.347$2,000.00$249.01$14,857.358$2,000.00$293.43$17,150.7837.First year: $33.56; second year: $109.64; third year: $190.4138.First year: $60.80; second year: $109.64; third year: $190.4139.$111,050.7740.$84,852.5141.$1,308.7542.$2,308.7543.(A) 1.540%(B) $202.1244.(A) 2.220%(B) $9,528.6445.33 months46.45 months47.7.77%48.6.14%49.0.75%50.0.84%51.After 11 quarterly52.After 66 monthly paymentsExercises 3.41.511/2562.97,656/78,1253.33,333,333/1,000,0004.111,111,111/1,000,0005.171/2566.90,909/100,0007.i=0.006;n=488.i=0.0495;n=249.i=0.02475;n=4010.i=0.0475;n=511.i=0.02525;n=3212.i=0.0206;n=2413.i=0.0548;n=914.i=0.009;n=3615.PV=$3,458.4116.PV=$13,133.8717.PMT=$586.0118.PMT=$232.0219.n=2920.n=7021.i=0.02922.i=0.01524.n=-lna1-i PVPMTbln11+i227.$35,693.1828.$55,135.9829.$11,241.81;$1,358.1930.$10,872.23; $1,727.7731.$69.58; $839.8432.$94.69;$2,181.4033.31 months34.36 months35.71 months36.57 months37.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 shouldbe $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 paymentswith 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; $17,319.6842.$1,167.57;$26,075.8843.PaymentNumberPaymentInterestUnpaidBalanceReductionUnpaidBalance0$5,000.001$706.29$140.00$566.294,433.712706.29124.14582.153,851.563706.29107.84598.453,253.114706.2991.09615.202,637.915706.2973.86632.432,005.486706.2956.15650.141,355.347706.2937.95668.34687.008706.2419.24687.000.00Totals$5,650.27$650.27$5,000.0044.PaymentNumberPaymentInterestUnpaidBalanceReductionUnpaidBalance0$10,000.001$1,821.58$260.00$1,561.588,438.4221,821.58219.401,602.186,836.2431,821.58177.741,643.845,192.4041,821.58135.001,686.583,505.8251,821.5891.151,730.431,775.3961,821.5546.161,775.390.00Totals$10,929.45$929.45$10,000.0045.First year: $466.05; second year: $294.93; third year: $107.8246.$3,319.0347.$97,929.78; $116,070.2248.$671.25; $145,65049.$143.85/mo; $904.8050.$42,033.0851.Monthly payment: $908.99(A) $125,862(B) $81,507(C) $46,90552.(A) $180,443(B) $139,061(C) $81,12253.(A) Monthly payment: $1,015.68; interest: $114,763(B) 197 months; interest saved: $23,49954.(A) $2,469.03(B) 9055.(A) 157(B) 243(C) The withdrawals continue forever.56.$522,241.29;$569,216.34; $668,430.6857.(A) Monthly withdrawals: $1,229.66; totalinterest: $185,338.80(B) Monthly deposits: $162.6558.$664.99; $240,301.8059.$65,58460.$68,29961.$34,69262.$40,227.6063.All threegraphs are decreasing, curve downward, and have the samexintercept; theunpaid 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 samexandyintercepts; the greater the interestrate, 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 Exercises1.A=$104.50(3.1)2.P=$800(3.1)3.t=0.75yr, 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)PeriodInterestAmount0$400.001$21.60$421.602$22.77$444.373$24.00$468.364$25.29$493.65(3.2)

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Solution Manual for Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences, 14th Edition - Page 18 preview image

A-16Answers19.To maximize earnings, choose 13% simple interest for investments lastingless than 9 years and 9% compound interest for investments lasting 9 years ormore.(3.2)20.$164,402(3.2)21.7.83%(3.2)22.9% compoundedquarterly, 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. Ifyou take the rebate, the monthly payments are $426.66. You should choosethe 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)PeriodInterestPaymentBalance1$100.00$100.002$5.40$100.00$205.403$11.09$100.00$316.494$17.09$100.00$433.58(3.3)PaymentNumberPaymentInterestUnpaidBalanceReductionUnpaidBalance0$1,000.001$265.82$25.00$240.82759.182265.8218.98246.84512.343265.8212.81253.01259.334265.816.48259.330.00Totals$1,063.27$63.27$1,000.0047.28 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 the360th payment is made. By reducing the principal, the loan would be paid offin 252 months. If the monthly payment were then invested at 7% compoundedmonthly, 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 interestpayments.(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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