Precalculus

A-2 Answers Section 1.4Section 1.4, page 571.d 20Midpoint (3, 3)3.y5.Midpoint6 (4, 5)54 a321(2, 3)d–1(–4 , 2)y3d 17( 2 3 , 3 2)a 8b 17c 8d 17a c, b d54321–2–3–4–554321–5–4–3 –2 –1 1 2 3 4 5–2–3–4–5y(8, 6)bc(6, 4)1 2 3 4 5 6 7 8(5, 4)(3, 3)(1, 2)–5–4–3 –2 –1 1 2 3 4 52(, 3 3 2)( )8,13xxx7.9.11.13.15.54 (2, 3)32a1 cx–5–4–3 –2 –1 1 b 5–2 (1, 0) (4, –1)–3–4–5a 10b 10c 20a 2 b 2 c 28 2 6 2 1000 2 (10) 2 100(52) 2 (52) 2 1002(2) 1 2( 4 3)( 4 3) 1 422 1 2 210501040103010201010(–0.1, 999)990980970y = 1000(x 3 + 1) 960yx y 1000( x 3 1)0.1 9990.0 10000.1 10010.2 10080.3 1027–0.5 –0.3 –0.1 0.1 0.3 0.5yy(0.3, 1027)(0.2, 1008)(0.1, 1001)(0, 1000)x54321–5–4–3 –2 –1 1 2 3 4 5–2–3–4–5x

17.19.–2–3–4–523. Center: (0, 0); radius: 22y54321–5–4–3 –2 –1 1 2 3 4 5–2–3–4–51064254321–5–4–3 –2 –1–11 2 3 4 5–2–3–4–521. Center: (0, 0); radius: 5yx52 + y 2 = 254321x–5–4–3 –2 –1 1 2 3 4 5y–10 –8 –6 –4 –2–22 4 6 8 10–4–6–8–10y2x 2 + 2y 2 = 16xxx25. Center: (4, 1) ; radius: 2y27. Center: (2, 3) ; radius: 2y29. Center: ( 3 ; radius: 22 , 1 )31.33.35.5(x + 4) 2 + (y – 1) 2 = 43(–4, 1) 21–5–4–3 –2 –1 1 2 3 4 5543x 2 – 4x + y 2 + 6y + 13 = 41–5–4–3 –2 –1 1 2 3 4 55434x 2 + 12x + 4y 2 + 8y = 31–5–4–3 –2 –1 1 2 3 4 5(– 3, –1)2(x 1) 2 (y 3) 2 16(x 4) 2 (y 3) 2 25(x 1) 2 (y 5) 2 1837. ii 39. iii 41. vi43. a. ii b. i c. iv d. iii45. a. i b. iii c. iv d. ii47. a. x 2b.c.49. a.b.c.51. x-intercepts:–2–3–4–5–2–3–4–5–2–3–4–5y(2, –3)(, 2)(2, )x 3, x 2(3, 2)(, 3) (2, )x 10.41, x 2.75, x 10.05y-intercept: y 1253. (4, 12)55. x 10.24, x 5.76xxxAnswers Section 1.4 A-3

A-4 Answers Section 1.557.Wage (dollars)Approximately $3.89 in 1991 (answers may vary), which is $0.36below the actual value of $4.2559. 117 2 12.82 blocks traveling on Lloyd Avenue from point Ato the point (3, 4) and then right to point B; 17 blocks traveling frompoint A to the point (5, 2) and then to point B.61. 300-5-50Approximately 199463. 90,000-2$6.00$5.00$4.00$3.00$2.00$1.00$0.00 1950 1960 1970 1980 1990 2000 2010–10,000Approximately 199365. a. x 2 (y 35) 2 30 2 b. Approximately 63.3 feet67. False 69. FalseSection 1.5, page 781. x 2 3. m 15 5. w 952137. a 3, a 4, a 6 9. x 3, x 2, x 211. s 0, s 3 13. y 1 3 15. u 217. y 10 19. s 6 21. No solution23. x 5 27 25. x 9 27. x 7 29. t 1 842 231. x 4 33. x 3 35. x 237. w 2 i39. m E 41. r A 43.c 2P 1t d 1 d 2d 2 d 145. 47. R 1 RR 2t v 0 v0 2 64s 64s 032R 2 R49. x 1.5 51. x 1.0, x 2.0 53. x 0.7555. x 11.99, x 11.99 57. y 4 3x; x 1.33451659.61.y x 2 2x 15 x 3.18, x 1.184 ;y 1 1 2x 6; x 5263. 97 65. 2 hours 45 minutes after the second car leaves67. Approximately 9.5 seconds 69. Approximately 19.8 miles71. September 199873. a.1 2t 0.1 second b. t 2 3 0.07 second4475. a. s dhl hb. s 110 feet23 4.7877. a. 6 hours b. 5 1 hours3c. 13 1 hours379. 26 2 miles per hour 81. True 83. True3Section 1.6, page 921.3.5.7.9.11.13.15.(, 13)(1, ) 1 4 , )(, )( 4 3 , )(2, 6) 1, 3 2 3, 9 2 5 2) , 17.1 2 3 4 5 6 7 8 919. x 6 21. u 2, u 3 23. No solution25. (3, 3) 27. (, 12) (12, ) 29. [3, 7]31. ( 7 33. 35. ( 1 6 , 3 2 , 9 2)2)37. x 1 5; (4, 6) 39.41.10-106 7 8 9 10 11 12 13 14–3 –2 –1 0 1 2 3 4 5–3 –2 –1 0 1 2 3 4 5–4 –3 –2 –1 0 1 2 3 4–2 –1 0 1 2 3 4 5 6–3 –2 –1 0 1 2 3 4 5 6 7]–1 0 1 2]]1 2 3 4 5 6 7]] 1, 7 3] 2x 3 6; (, 9 2) ( 3 2 , )-10The x-intercepts; x-values where y is positive,x-values where y is negative43. x 2.4, x 6 45. [3, 1] 47. [5, 1]49. (22, 22) 51. Approximately (, 1.22) (0.72, )53. (, 1) 55. x 3 57. [2, 0] [2, )2 , x 2 759. From 141.15 to 205.26 miles10

Answers Chapter 1 Review A-561. Between 13.4 and 13.6 inches63. From 98.6 to 102.2 degrees Fahrenheit65. Between 2 and 3 seconds67. From 49.3 seconds to 200.7 seconds after blast-off69. False 71. TrueSection 1.7, page 1081. 49223. 11 5. 7. 9.5 51 13 1.6911. 1,000,000 13. 3 15. 4 17. 3 19. 5 321. Slope of l 1 2Slope of l 2 2 3Slope of l 3 3Slope of l 4 023. Slope of l 1 3 7Slope of l 2 7 3Slope of l 3 3 725. y x 2 27. y x 10 29. x 331. y 5x 11 33. y 1 35. y 1 3 x 116337. y 2x 4 39. x 3 41. y 0.7353x 2.517643. y 320 x 174045. x 47. m 2 3 , b 8 349.54321–5–4–3 –2 –1 1 2 3 4 5–2–3–4–5m 1 3 , b 4 354321–5–4–3 –2 –1 1 2 3 4 5–2–3–4–5yy2x – 3y = 8x = 3y + 4xx51.321x–5–4–3 –2 –1 1 2 3 4 5–2–3 y – 3 = – 2(x + 3)–4–553. y 2 55. y 4x 5 57. y 3x 23 x 259. x 3 61. 3x y 4 63. 2x y 1 or 6x 3y 1365. ( 13 67. (2, 5) 73. C 5N 10005 , 14 5)75. a. h 264 b. Approximately 3 inches67 tc. Approximately 50 inches77. $146,00079. a. 271.4 million b. 313 million81. False 83. True 85. FalseChapter 1 Review, page 1131. Rational, real, complex 3. Complex5. [5, 1)7.m 2, b 3y(, 1 2t 1/2(t 4)(t 8)9. 81 11.b 4 13. 3.14 10 7 15. a 2 bb3 17. 3319.x 2x 2 221. 2s 3 t3 23. 117 25.3b27. x 2 29. x 1/12 31. 33. t 3 t 2 5ta35. 3w 2 10w 8 37. (3u 2)(3u 2) 39.41.1 t 2(y 1)43. 45. t 1(3x 1) 2 47.x 3 t(t 1) y(y 2)49.x151.(x 1)(x 3) 2t53.y54321–5–4–3 –2 –1 1 2 3 4 5(–2, –3)54–7 –6a 2–2–3–4–5–2d 10Midpoint (1, 1)]–5 –4 –3 –2 –1 0–1(4, 5)(1, 1)]0 1 2 3x1

A-6 Answers Section 2.155. Center: (0, 0); radius: 4y54321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–557. Center: (5, 4) ; radius: 3x 2 + y 2 + 10x – 8y + 32 = 0–8 –7 –6x 2 + y 2 = 16(–5, 4)–4 –3 –2 –18765432159. (x 2) 2 (y 5) 2 9 61. iv 63. ii65. x-intercepts: x 3.79, x 1.03, x 10.26; y-intercept: y 567. (2, 3) 69. x 5 71. x 7 34–573. x 3, x 0, x 1 75. x 3, x 4277. w 2 2 79. y 1 81. x 22 , y 2 383. x 1 85. x 2 87. a 23 , x 289. x 1.14 91. x 0.33, x 1.5493. y 4 2 95. y x 4 5; x 53 x; x 6xyx97.99.101. (, 10)103. (, )105.y 2 x 1; x 5(4, )( 2 3 , 2 )–6 –5 –4 –3 –2 –1 0 1 2–13 4 5 6 7 8 9 10 11–4 –3 –2 –1 0 1 2 3 4107. (, 5) (1, )1109. (0.47, 1.40) 111. 113. 4 115. y 3x 23117. y 2x 4 119. y 2x 2 121. y 3x 22123. y 3 2 x 4125. a. 4x 2 12xy 9y 2 b. 2x 3y127. a. (0, 7) b. (2, 11)129. a. (x 3)(x 2) b. x 3, x 2131. a. x 3 9x 2 9x 81 b. Z 9, Z 3, Z 3133. 84,375,000 cubic feet; approximately 1055 135. $11.50137. Between 25 million and 75 million units139. Approximately 1.3 hours for Roberto and 2.3 hours for DanielChapter 1 Test, page 1180121. True 2. True 3. True 4. False 5. True6. True 7. False 8. False 9. 2, for example10. x 2 2x 1, for example 11. x 2 6x 9 0, for example12. b, for example 13. x 1 0a 10 14. 3x 2 y 3 3x3x 115. 2 16. 6x 2 5x 6 17.x(x 2)18. (2x 3)(2x 3) 19. (u 2v)(u 2 2uv 4v 2 )20. (, 1) (2, ) 21. x 1.71, x 1.3522. x 1 5 23. [1, 5] 24. x 4 25. x 226. y 3 4 x 19427. a. ii b. i c. iii28. 24 feet; the ball hits the ground after 2.75 seconds3Chapter 2Section 2.1, page 1301. Function 3. Not a function 5. Function7. y is a function of x. 9. y is not a function of x.11. y is a function of x. 13. y is a function of x.15. y is not a function of x. 17. y is a function of x.19. a. 12 b. 2 c. 221. a.14 17 3t 2b. c.11 15 4t 523. a.753t 4 b. 3t 2 6t 3 c.t 225. a.1x 2 b. x 4 2x 2 1 c.a 227. a.1 1 1b. c.8 t 2 1 x 229. h(x) 31. f(x) 1x x 333. All real numbers35. All real numbers except 437. All real numbers except 3 and 339. [1, )41. All real numbers in [2, ) except 1 and 343. All real numbers except 3 and 345. f(x) 2x 1, for example47. f(x) 1 , for examplex 149. f(x) 7 x, for example51.1f(x) , for examplex(x 3)

Answers Section 2.1 A-753.x f(x) 2x 50 52 14 35 (0, 5)43 ƒ(x) = –2x + 521 (2, 1)x–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5y(4, –3)c.10-10-10Domain: ( , )Range: [1, )d.5-510555.x f(x) (x 1) 2 33 12 21 30 21 1y59. a.-5Domain: ( , )Range: (0, 1]1057. a.54321ƒ(x) = (x + 1) 2 – 3–5 –4 –3 –2 –1 1 2 3 4 5(–2, –2) –2 (0, –2)–3(–1, –3)–4–510xb.-10-10Domain: ( , )Range: [1, )1010-1010-1010b.-10Domain: ( , )Range: [0, )10c.-10Domain: ( , )Range: (0, )10-1010-1010-10Domain: ( , )Range: [0, )-10Domain: ( , )Range: ( , )

A-8 Answers Section 2.2d.10c.y[2, )Domain: ( , )Range: ( 1, 1)61. 4 63. 765. a. x 2 y 2 b. y 2 c.67. V 69. A 2r 71. A a 26 d 3 22(a 2)73. V x(16 2x) 2 ; the domain is the set (0, 8).75. V (8.603 10 38 )t 3 ; 4.358 10 43 cubic miles77. R(x) 2 5 x 220 79. False 81. FalseSection 2.2, page 15219. a.b.21. a.-10y-10g(x) 1 4 x 4 1 3 x 3 x 2g(x) 1 4 x 4 1 3 x 3 x 2101. x 1 33. x 2, x 4 5. x 5 27. x 2, x 2 9. a 311.13.x 2.56, x 0.10, x 3.96x 2.34, x 0.61, x 0.1415. x 1.24, x 3.2417. a. g(x) x 2 b.c. g(x) x 2 2g(x) x 1d.e.54321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–554321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–554321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5yyh(x) = ƒ(x + 1) – 4h(x) = ƒ(–x)h(x) = –ƒ(x) + 2xxxb.54321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5yh(x) = ƒ(x – 2)xf.5432h(x) = –ƒ(x – 1)1x–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5y54321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5h(x) = ƒ(x) + 3x23. a.h(x) = ƒ(x – 3) + 2y54321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5x

Answers Section 2.2 A-9b.yb.y54321–2–3–4–5h(x) = ƒ(–x) – 1–5 –4 –3 –2 –1 1 2 3 4 5x54321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5xc.d.54321–2–3–4–554321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5h(x) = ƒ(–x + 2) – 325. Even 27. Odd 29. Neither31. a.y54321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5y–5 –4 –3 –2 –1 1 2 3 4 5yh(x) = –ƒ(x + 1)xxx33. a.b.54321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–554321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5yy35. Increasing: (2, )Decreasing: (, 2) Turning point: local minimum at (2, 1)37. Increasing: (, 0.62), (1.62, )Decreasing: (0.62, 1.62)Turning points: local maximum at (0.62, 7.09), local minimum at(1.62, 4.09)39. Increasing: (, 2)Decreasing: (2, )Turning point: local maximum at (2, 5)41. Increasing: (1.30, 0.17), (1.13, )Decreasing: (, 1.30), (0.17, 1.13)Turning points: local minimum at (1.3, 3.51), local maximum at(0.17, 0.08), local minimum at (1.13, 1.07)43. Q(x) (x 5) 2 14(x 5) 10045. g(t) 16t 2 80t 20; the graph of g is the graph of f shifted20 units upward47. Approximately 30 or 270 systems per month to break even; 150systems per month to maximize profit49. (2, 3 51. 50 feet 100 feet2)xx

Answers Section 2.5 A-1145. a.b. B(t) 10t 2 60t 2700Total production is virtually constant.Maximum: 2790Minimum: 2700b. g(n) 113 1 (assuming a hot dog and bun weigh one fourth4 nof a pound)c. ( f o g)(t) 2524 t 282525; (g o f )(t) 6 24 t 113d. (g o f )(t) represents Kobayashi’s weight after t minutes.47. False 49. FalseSection 2.4, page 1781. Inverses 3. Not inverses5. Inverses 7. Inverses9. Inverses 11. 1–113. Not 1–1 15. 1–117. Not 1–1 19. Not 1–121. 1–1; f 1 (x) 3x 323. Not 1–125. 1–1; f 1 (x) x 1, x 1127. 1–1; f 1 (x) (x 2 5), x 0 29. Not 1–1231. 1–1;x f 1 (x)33. Not 1–135.Production25002000150010005001 2 3 4 5 6 7f(t) 25 t, 0 t 1264 07 110 213 316 4f 1 5y = ƒ(x) 4 y = ƒ –1 (x)37. does not exist.321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5yB(t)xMonth39.41. a. M(t) 98 0.12t b. 110°F c. M 1 (t) 8.33t 817d. M 1 (t) gives the year (after 1935) in which the maximum temperatureis t°F. For example, since M 1 (120) 183, this modelpredicts that the maximum temperature will be 120°F in 2117.43. a. 4 yearsb. f 1 (t) 72 approximates the interest rate at which an amountttakes t years to double.c. 9%45. a. Yes; the formula suggests a maximal weight of 195 pounds.b. Assume h 0; f 1 (w) 5.30548w gives the maximumheight required for a person of a given weight to not be overweight.16 1 254321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5c. About feet tall d. Answers may vary.47. False 49. TrueSection 2.5, page 1921. Quadratic 3. None 5. None 7. Linear9. Linear 11. Piecewise13.y54321 f(x) = 2x – 1x–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5Slope 2; y-intercept 115.y5432h(x) = – 3x 14+ 4x–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5yy = ƒ –1 (x)y = ƒ(x)xSlope 3 ; y-intercept 14

A-12 Answers Section 2.517. h(x) 1 19. g(x) 4 2 x 53 x 421. (0, 4)31.33.( 3 2 , 11 2)23. 25. (8, 54) 27. (1, 0)29. f(x) 2(x 1) 2 3yy = ƒ(x)6(0, 5)4g(x) (x 3) 2 1y2–4–664–654321–2–3–4–5y(1, 3)–6 –4 –2 2 4 6–2x = 32(3, –1)x–6 –4 –2 2 4 6–2(2, –2)–4f(2) 2; f(0) 4; f(3) 2–5 –4 –3 –2 –1 1 2 3 4 5xx37.39.41.43.f(3) 3; f(1) 1; f(4) 6yy = h(x)-5y = ƒ(x)y = h(x)54321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–554321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–554321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5yy5xxxy=(x-2) 2535.h(0) 1; h(2) 2; h(4) 3yy-5 y=-x 2 +2xy = h(x)54321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5xy = ƒ(x)54321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5x

Answers Section 2.6 A-1345.5 y=x 3 -2x 2 +2c.y-547. a 2 49. a 251.y53. a.b.y=x 3 +2x 2 554321–2–3–4–5y–2–3–4–5-554321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–554321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5yyy = g(x)–5 –4 –3 –2 –1 1 2 3 4 554321 f (x) = x + 2 ⎦x–5 –4 –1 1 2 3 4 5⎦xxx55. a. i. g(2.8) 0.8 ii. g(4.7) 0.7 iii.b.c. x57. a. C(x) 80x 5000, where x is the number of units rentedb. p 5x 550 c. R(x) 5x 2 550xd. P(x) 5x 2 470x 5000 e. 47 units at $315 per month59. a. 81.13 feet b. Yes61. In 1960; approximately 1.14 billion acres63. Cost432154321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–554321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5C(x) = 0.25 – 0.15 1 – x⎦Minutes5 10 15 2019 minutes65. $34,211.75 for filing separately; $34,210.50 for filing jointly67. MATH ROCKS 69. False 71. TrueSection 2.6, page 210yg(x) = ((x))⎦x 31. 4 3. 48 5. 10 7. 12 9. 60 11.2436413.18f (x) x 2 15. f(x) x 2 4x 17. h(x) x 2 3x 519. y 0.5x 2.33 21. y 1.6x 4.823.25.y 2.5x 90; y 152.5 when x 25y 31.55x 77.51; y 17.14 when31. 5.75 10 25 newton 33. 3000 pounds27. 2592 board feet 29. 800,000 joules35. y 2.0822x 73.181; 281.4 kilogramsxxg( 235) 3 5

A-14 Answers Chapter 2 Review37. y 9.5714x 177.14, where y is the CFC-11 concentration inparts per trillion and x is the number of years after 1980; approximately387.7 parts per trillion; the model doesn’t take into accountthe effects of global effort to cut usage of CFCs to preserve theozone layer.39. y 0.75x 2 34.8x 320, where x 0 corresponds to 1980;1,659,000 inmates41. True43. FalseChapter 2 Review, page 2161. Function 3. Not a function5. Defines y as a function of x7. Does not define y as a function of x9. a. 21 b. 28x11. a. 2 xb.2 2x 1x 2 1 x 2 2x 213. a. 4 b. 1 c. a 415. All real numbers17. ( 1 2 , )19.10-10-10Domain: (. 2] [2, )Range: [0, )21.10-10-10Domain: all real numbers except 1Range: {1, 1}23. a. g(x) 2x 3 6x 1b. g(x) 2x 3 6x 2 325. a.h(x) = f(x + 3) y54321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–51010xb.c.27. Odd29. Neither31. x 9 433. x 8 335. a. x 1.88, x 0.35, x 1.53b. Turning points: local maximum at (1, 3), local minimum at(1, 1)c. Increasing: (, 1) (1, )Decreasing: (1, 1)37. a. x 1.73, x 1.73b. Turning points: local maximum at (1, 1), local minimum at (3, 3)c. Increasing: (. 1) (3, )Decreasing: (1, 2) (2, 3)( f g)(x) x 2 2x 1( fg)(x) 2x 3 x 2c. ( f/g)(x) x 22x 1 ; x 1 2d. ( f o g)(x) 4x 2 4x 1e.39. a.b.41. a.b.c.(g o f )(x) 2x 2 1( f g)(x) 1x 4 x 3 ; x 4( fg)(x) x 3x 4 ; x 4(f/g)(x) 54321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–554321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5h(x) = – f(x) – 21x 4 4x 3; x 4, x 0d. ( f o g)(x) 1x 3 4 ; x 431e. (g o f )(x) (x 4) 3; x 4yyh(x) = f(x – 2) + 1xx

Answers Chapter 2 Review A-1543. a. ( f g)(x) 2x 2 2x 4; x 2b. ( fg)(x) 2x 2 2x 4; x 2c. (f /g)(x) 2x 22x 4 ; x 2d. ( f o g)(x) 4x 8; x 2e. (g o f )(x) 4x 2 445.x ( f g)(x) (fg)(x) (f/g)(x) (f o g)(x) (g o f )(x)63. None-101010Domain f g: {0, 1, 2, 3}Domain fg: {0, 1, 2, 3}Domain f/g: {0, 1, 3}Domain f o g: {0, 1, 2, 3}Domain g o f: {0, 1, 2, 3}47. Inverses 49. Not inverses 51. 1–1; f 1 (x) x 2353. Not 1–1 55. 1–1; f 1 (x) x 2 4, x 057. 1–1;59.0 4 330 21 4 4 1 3 02 3 0 Undefined 1 13 1 0 0 2 361. Quadraticx2f 1 (x)15 210 317 426 554321–2–3–4–51–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5–6–7–8yyy = f –1 (x)–5 –4 –3 –2 –1 1 2 3 4 5y = xy = f(x)h(x) = –(x – 3) 2 + 1x-intercepts (2, 0) and (4, 0); y-intercept (0, 8)xx1x-intercept ( 2, 0); y-intercept (0, 1)65. Piecewise67.x-intercepts ( 3 and (5, 0) ; y-intercept (0, 3)2 , 0 )Vertex (1, 4) ; x-intercepts (3, 0) and (1, 0); y-intercept (0, 3)69.g(x) = –x 2 + 8x – 17y15105–15 –10 –5 5 10 15–5–10–1554321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5g(x) =54321–5 –4 –3 –2 –1 1 2 3 4 5–2–3(–1, –4) –4y-10f(x) = (x + 1) 2 – 4y(4, –1)2x + 3 x 15 – x 2 x >1Vertex (4, 1) ; no x-intercepts; y-intercept (0, 17)71. f (x) 1 73. h(x) (x 2) 2 12 x 3xxx

Answers Section 3.5 A-1723.80q(x) 4x 3 1 , r(x) 3 x 2 1 9 x 127 8125. f(x) (x 5)(x 2)(x 1) ; Zeros: 5, 2, 127. p(x) (2x 1)(x 2)(x 3) ; Zeros: 1 , 2, 3229. g(x) (x 4) 2 (x 2)(x 1) ; Zeros: 4, 2, 131. h(x) (3x 2)(2x 1)(x 1)(x 8)Zeros: 2 1, 83 , 1 2 ,33. a. 39 b. 6 c. 435. a. 12 b. 1608 c. 88.266337. a. 14 b. 3339. False 41. TrueSection 3.3, page 2561. f(x) (x 3)(x 2)(x 2) ; Zeros: 3, 2, 23. f(x) (x 1)(2x 1)(x 5) ; Zeros: 1, 1 , 52x 2 x 125. f(x) (x 4)(3x 1)(x 1) 2 ; Zeros: 4, 1 , 137.2f(x) (x 2)(x 1)(5x 2) ; Zeros: 2, 1,59.1f(x) (x 2)(2x 1)(3x 1) ; Zeros: 2, , 1 2 311. f(x) (x 1)(x 2)(x 2 3) ; Zeros: 1, 2, 313. f(x) , for example15. f(x) 1(x 5)(x 1)(x 2)217.1f(x) x 2 (x 2) 2319. f(x), for example21. f(x) x 2 2x 3 23.1f(x) (x 4)(x 2)2425.27.f(x) (x 2)(x 1)(x 1)(x 2)f(x) (x 3)(x 2i)(x 2i) ; Zeros: 3, 2i, 2i29. f(x) (x 1 i)(x 1 i)(x 4)(x 1) ;Zeros: 1 i, 1 i, 4, 131. Zeros: i, i; f(x) (x i)(x i)33. Zeros: 0, 1 2i, 1 2i;f(x) x(x 1 2i)(x 1 2i)35. Zeros: 1, 1, 2i, 2i; f(x) (x 1)(x 1)(x 2i)(x 2i)37. Zeros: 0, 1, 2 i, 2 i;f(x) x 2 (x 1)(x 2 i)(x 2 i)39. f(x) (x 2)(x 2 4) , for example41. f(x) (x 2 1)(x 2 2x 2) , for example43. f(x) x(x 2 2)(x 2 4x 8) , for example45. Zeros: 0, 8, 10; Domain: (0, 8); Original dimensions: 20″ 16″47. Profit is zero at 100 or 300 frames per month and is positivebetween these two values.49. s(t) 16t 2 80t 64; 36 feet 51. False 53. False (x 1) 3 (x 1 2) 2Section 3.4, page 2671. Possible rational zeros: 1, 3, 9, 27; Actual rational zeros:3, 33. Possible rational zeros: 1, 2, 3, 4, 6, 12; Actual rationalzeros: 2, 2, 31 15. Possible rational zeros: 1, 2, 2, 4; Actual rational zeros:1, 1 2 , 1 2 , 27. Possible rational zeros: 1, 3, 1 2 , 3 2Actual rational zeros: 3 2 , 1, 19. Possible rational zeros: 1, 2, 3, 4, 6, 12, 1 2 , 3 2Actual rational zeros: 1, 3 2 , 411. Number of positive zeros: 0; Number of negative zeros: 113. Number of positive zeros: 0; Number of negative zeros: 015. Possible number of positive zeros: 1 or 3; Actual number of positivezeros: 1; Number of negative zeros: 017. Number of positive zeros: 1Possible number of negative zeros: 0 or 2Actual number of negative zeros: 019. Possible number of positive zeros: 0 or 2Actual number of positive zeros: 2Number of negative zeros: 127. 6, 1, 1 29. 1, 12 31. 3, 1 6 , 1 233. 1 35. 11, 118 , 2, 237.x 2, x 1, x 239. x 3, x 3 41. x 1, x 1 2 , x 1 43. 0.3245. 1.49, 0.80 47. 11.0049. 1.5 inches 1.5 inches 4 inches51. The square should have a side length of either 0.5 inch or approximately1.7 inches.53. 1968, 1984, and 199855. a. 1100v 1 1100v 2 1100v 3b. Solutions of the equation 1100v 1 1100v 2 1100v 3 3000correspond to zeros off (v) 1100v 1 1100v 2 1100v 3 3000By Descartes’ Rule of Signs, there is exactly one positive valuefor v.c.57. a.v 0.953, r 4.9%p 1 v 1 p 2 v 2 p 3 v 4 b. 1000v 0 dv 2c. Either 2 or 4 interest ratesd. r 15.9%, r 197.3%59. True 61. FalseSection 3.5, page 2811. Domain: all real numbers except 2; Zeros: none; graph: vii3. Domain: all real numbers except 0; Zero: 1; graph: iii5. Domain: all real numbers except 2; Zeros: none; graph: iv7. Domain: all real numbers except 1 and 1; Zeros: 2; graph: ii9. a.yg(x) =1x – 354321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5x

A-18 Answers Section 3.5b.yc.y54321–2–3–4–51g(x) = x+ 2–5 –4 –3 –2 –1 1 2 3 4 5x54321–5 –4 –3 –2 –1 1 2 3 4 5g(x) = –f(x)–2–3–4–5xc.g(x) = – 1 x54321–2–3–4–5y–5 –4 –3 –2 –1 1 2 3 4 5x13.yx = 454321y = 0–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5x11. a.54321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5yg(x) = f(x – 1)x15.y = 2x = –154321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5yxb.54321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5yg(x) = f(x) – 2x17. Vertical asymptote: x 3Horizontal asymptote: y 0yx = –3543211f(x) =x + 3y = 0–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5x

Answers Section 3.5 A-1919. Vertical asymptote: x 2Horizontal asymptote: y 1h(x) =y = 121. Vertical asymptote: x 2Horizontal asymptote: y 3yy = 3x = 223. Vertical asymptotes: x 3, x 3Horizontal asymptote: y 0y = 0xx + 2x = –387654321–2x = –2y54321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–554321–2–3–4–5g(x) =x = 325. Vertical asymptote: noneHorizontal asymptote: y 5yyf(x) =3xx – 2–5 –4 –3 –2 –1 1 2 3 4 5 6 7xx 2 – 9–5 –4 –3 –2 –1 1 2 3 4 5xxx27. Vertical asymptote: x 1Horizontal asymptote: y 0y = 0–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5x = –129. Vertical asymptote: x 2Horizontal asymptote: y 1y = 154321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–531. Vertical asymptote: x 0Inclined asymptote: y 2x5432154321y1h(x) =(x + 1) 2yf(x) =x = 2g(x) = 2x + 1 xy = 2x–5 –4 –3 –2 –1 1 2 3 4 5–2 x = 0–3–4–5yx 2(x – 2) 2xxxy = 57654321–2g(x) =45x29x 2 + 1–5 –4 –3 –2 –1 1 2 3 4 5x

A-20 Answers Section 3.533. Vertical asymptote: x 1Inclined asymptote: y x 1y–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4f(x) =x 2–5x – 1x = 135. Vertical asymptote: x 2Inclined asymptote: y 3xy37. Horizontal asymptote: y 0yy = 039. Vertical asymptote: x 15Horizontal asymptote: y 12h(x) =12x + 24y x – 15y = 125040302010–40 –20 –10 10 20 30 40 50–20–30–40–50x = 15987654321–5 –4 –3 –2 –1–1x = –254321–254321g(x) =1 2 3 4 5y = –3xy = x + 1f(x) =2x 2 + 1–5 –4 –3 –2 –1 –11 2 3 4 5–2–3–4–5xx–3x 2 – 6x + 1x + 2xx41. Vertical asymptote: x 3Inclined asymptote: y x 1–10 –8 –6 –4 –2 2 4 6 8 10–2–4 x = 3–6–843. Vertical asymptotes: x 3, x 3Horizontal asymptote: y 0yy = 0h(x) = –1x 2 – 945. Vertical asymptote: x 3y47. y 2 49. y 351. Vertical asymptote: x 100Horizontal asymptote: y 0.001A 75% reduction; 100% reduction is unattainable according tothis model.xf(x) =1000(100 – x), x 00.0050.0040.0030.0020.001–0.001x = –3x 3f(x) =x – 380604020–5 –4 –3 –2 –1 1 2 3 4 5–20–40–60–8012108642y54321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5g(x) =x = 310 20 30 40 50 60 70 80 90x 2 – 4x + 7x – 3y = x – 1x = 3xx = 100xxy = –0.001

Answers Chapter 3 Review A-2153. Vertical asymptote: noneHorizontal asymptote: y 0Approximately 7 and 13 years; unemployment rate decreases as educationincreases; 0% unemployment is unattainable according to thismodel.1510555. Horizontal asymptote: y 100The average cost approaches $100 as the number of bicyclesincreases.500400300200100f(x) =77, x > 0(x – 10) 2 + 75 10 15 20 25C(x) =100,000 + 100x, x 0xy = 100500 1000 1500 2000x = 057. a. 58 balls should be ordered 10 times per year.b. Inclined asymptote: y 3 ; as the number of balls2 x 600ordered gets very large, the inventory cost increases by roughly$1.50 for each additional ball ordered.59. False 61. TrueChapter 3 Review, page 287y = 01. g(x) → as x → or 3. f(x) → as x → , f(x) → as x → 5. h(x) → as x → or 7. Zero: 9.11; Turning points: local maximum at (0.00, 3.00), localminimum at (6.00, 39.00)9. Zeros: 13.12, 3.12; Turning points: local minimum at(9.61, 417.63), local maximum at (0.13, 3.94), local minimumat (1.98, 8.40)11. q(x) 2x 1, r(x) 013. q(x) x 2 4x 11,r(x) 44x 215. q(x) 3x 2 5x 2, r(x) 017. q(x) 2x 3 6x 2 14x 43,r(x) 13219. a.2558b. 1021. a. 610 b. 223. Zeros: 3, 1 225. Zeros: 3, 2 27. Zeros: 1, 1 2 , 1 329. f(x) x 3 6x 2 x 30, for example31.33.35.f(x) 4(x 1) 2 (x 1) 2f(x) x 3 3x 2 x 3f(x) x 3 3x 2 16x 48, for example37. f(x) (x 2 i)(x 2 i) ; Zeros: 2 i, 2 i39. h(x) (x 3)(x 3)(x 4i)(x 4i) ; Zeros: 3, 3, 4i, 4i41. Possible rational zeros: 1, 2, 3, 6; actual rational zeros:2, 1, 31 1 3 343. Possible rational zeros: 1, 3, , , , 2 4 2 4Actual rational zeros: 1, 1 2 , 1, 3 245. Number of positive zeros: 0; Number of negative zeros: 147. Number of positive zeros: 1; Possible number of negative zeros: 2 or0; Actual number of negative zeros: 251. x 1, x 2, x 6 53. x 2 3 , x 1 4 , x 455. 2.13, 0.20, 2.33 57. 21.00, 1.5259. Domain: all real numbers except 3; Zeros: none; graph: iv61. Domain: all real numbers except 3 and 3; Zero: 2; graph: i63. Vertical asymptote: x 2Horizontal asymptote: y 0yx = –2y = 065. Vertical asymptote: x 1 3Horizontal asymptote: y 2 3y2x + 5g(x) =3x – 1y = 2 354321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–554321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–51f(x) =x + 2x = 1 367. Vertical asymptote: x 0Horizontal asymptote: y 0y54321–2–3–4–5f(x) =3 – xx 2y = 0–5 –4 –3 –2 –1 1 2 3 4 5x = 0xxx

A-22 Answers Chapter 3 Test69. Vertical asymptote: noneHorizontal asymptote: y 2y71. Vertical asymptote: x 1Horizontal asymptote: y 0yy = 073. Vertical asymptote: x 0Inclined asymptote: y 2xyy = –2x54321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–575. Vertical asymptote: x 3Inclined asymptote: y 3x 1y5040302010–8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5x = –354321–2–3–4–52f(x) =(1 – x) 2h(x) = – 2x –x = 0h(x) =–20–30–40–50y = 2–5 –4 –3 –2 –1 1 2 3 4 52xg(x) =2x 2 + x + 254321–4 –3 –2 –1 1 2 3 4 5–1–2–3–4–5x = 11xx3x 2 + 8x – 9x + 3y = 3x – 1xxx77. a.x 2 4x 5x 1b. y x 379. a.3 133 13x b. x , x 02281. a. x 2 4x 4 b. (x 5) 9x 183. a. Vertical asymptote: x 3; Horizontal asymptote: y 2b.85. a.h(x) 1x 3 2(2 3i) (2 3i) 4,(2 3i)(2 3i) 13b. f(x) x 2 4x 1387. f(x) 31000 x 2 18x 15,000The largest profit of $12,000 occurs when x 3000.89. Zeros: 2, 10.3; The months when the average temperatureis zero91. yChapter 3 Test, page 2921. True 2. True 3. False 4. False5. True 6. True 7. False 8. True9. f(x) x, for example10. f(x) x 3 6x 2 5x 12, for example11. f(x) x 3 2x 2 9x 18, for example12. f(x) x 4 1, for example13.xf(x) , for examplex 114. f(x) x 3 1 , for examplex 215. f(x) x 2 (x 4)(2x 1) ; Zeros: 0, 4, 1 216. f(x) (x 2)(3x 1)(2x 3)17.18.706015,000 + 20x50 C(x) =x403020y = 2010x1000 2000 3000x = 0The average cost approaches $20.Zeros: 2, 1 3 , 3 2q(x) 3x 3 6x 2 5, r(x) 4f(x) x(5x 2)(x 3i)(x 3i)Zeros: 0, 2 , 3i, 3i519. Possible rational zeros: 1, 3, 9, 1 2 , 3 2 , 9 2Actual rational zeros: 3, 1, 3 220. Possible number of positive zeros: 3 or 1Actual number of positive zeros: 1Number of negative zeros: 121. Approximately 1.52

Answers Section 4.1 A-2322. Vertical asymptote: x 3 2Horizontal asymptote: y 1 2yy = 1 254321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5x + 1f(x) =2x – 3x = 3 2x23. a. Approximately 1988 and 1994b. The rate peaked at approximately 9.6 per 100,000 in 1991.c. The crime rate dropped for 1991 through 2000.Chapter 4Section 4.1, page 3041.y3. a 1 35.7.a 10y54321–2–3–4–5f(x) = 3 x–5 –4 –3 –2 –1 1 2 3 4 5xg(x) = e –x54321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5xa. b.54321–2–3–4–5c. d.54321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5y–5 –4 –3 –2 –1 1 2 3 4 5yg(x) = –3 xg(x) = 3 x + 2xxg(x) = 3 –xg(x) = 3 x + 254321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–554321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5yyxx9.54321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5yg(x) = e x – 211. t 11.79 13. t 49.70 15. x 4 17.19. x 3 21. x 5 23. x 2, x 125. a. $1790.85 b. $1814.02 c. $1819.40d. $1822.03 e. $1822.1227. 20 gerbils initially present;t f(t)0 201 302 453 684 101approximately 228 gerbils after 6 months;approximately 735 billion gerbils after 5 yearsxx 3

A-24 Answers Section 4.229. $20,805.70; $21,103.4831. Approximately 25.96 quadrillion Btu in 1940; approximately 101.59quadrillion Btu in 2000; approximately 291.3% increase; approximately127.53 quadrillion Btu in 201033. Approximately 4.64 hours35.0.5-4-0.2Maximum at approximately (0, 0.40); f (x) approaches 0 as xapproaches 37. a. Approximately 130 students after 2 days; approximately 190students after 5 daysb. 1100-5-100c. Approximately 24 daysd. N(t) approaches 1000 as t approaches .39. True 41. TrueSection 4.2, page 3181. 2.72130 3. 0.17609 5. 0.53959 7. 0.708779. 4 11. Undefined 13. 2 15. 3 17. 219. 3 21. 100 23. 7 25. 2.24 27. 5.6429. 6.75 31. 2 2 1 433. 10 3 100035.37.e 2 x 1x 3 10 39. log 3 9 2 41. log 1/2 8 343. ln 5 x 45. ln 1 2 0.013t47. Domain: (0, )54321–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5yg(x) = –ln xx44049. Domain: (3, )–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–551. Domain: (, 0)53.55.543215432g(x) = ln(–x) 1 – 1–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5f 1 (x) 3 x54321–5 –4 –3 –2 –1 1 2 3 4 5–2 f(x) = log 3 x–3–4–5f 1 (x) ln(x 5)54321f –1 (x) = ln(x + 5)x–5 –4 –3 –2 –1 1 2 3 4 5–2–3–4–5yyyyg(x) = ln(x – 3)f –1 (x) = 3 xf(x) = e x – 5xxx

Answers Section 4.5 A-2557.59.10f 1 (x) x 10x31000f(x) = log(1000x)-1-1Domain: (0, )61. 10-2554321–2–3–4–5y–5 –4 –3 –2 –1 1 2 3 4 5f –1 (x) = 10x1000-2Domain: (1, )63. Approximately 49.7 minutes 65. Approximately 13.4 hours67. Approximately 20.4 decibels 69. 100 decibels71. Approximately 3.55 73. Approximately 4.575. 25 times77. a. 60 wpm in approximately 4.6 weeks; 80 wpm in approximately8 weeksb. The time gets larger without bound; noc. 20510x11. ln x 3 y 413. ln 15. log 17. 3 x z64z(x z) 2319. x 27 21. x 2 23. x 253 25.x 027. x 1 329. x 2 31. x 6 1 33. x 9535. x 1 37. No solution 39. x 999 41. All43. x e e ln 16ln 0.34145. 47.ln 3 2.52372 ln 12 0.4329649.ln 1051. 0.16, 3.15 53. 0.04, 1.50ln 2.0114755. 11.42, 2.97, 0.59 57. 10,000 times more intense59. 30 decibels 61. Approximately 586.8 tons63. Approximately 177.8 times more energy 65. False67. True 69. True 71. TrueSection 4.4, page 3421. x 4 3. x 1log 105. x log 7 1.18329log 11log 367. x 9. x log 18 2.79758log 3 2.18266 5111. x ln 213. x 1 ln 2 2.25889 2(1 ln ) 3.4547115. x 1317. t log 1.06 118.5495919. x 0.69, x 1.10 21. x 0.5723. x 4.48, x 2.11,x 0.3525. Approximately 10.2 years 27. r 5.78%29. February 2008 31. February 206133. Approximately 237.63; the year 201735. At approximately 6:33 A.M. on July 7, 200337. Approximately 122,269 39. Approximately 11,520 years41. Approximately 5.2 years 43. True 45. FalseSection 4.5, page 3551. a.Rabbits6050403020101 2 3 4 5 6Monthln x 3x 2x 1532-10110-2Domain: [0, 100)79. True 81. False 83. TrueSection 4.3, page 3301. 2lnx lny 3. 3log 5 x 4log 5 y 3log 5 z15. 1 ln7 3lnx 7. 9.4 log x 1 log y log z2log x y 2b.Rabbits6050403020101 2 3 4 5 6Month

A-26 Answers Section 4.5c.RabbitsLargest absolute error: 41,420Sum of the absolute errors: 92,621The population in 2010 will be approximately 870,368.The population will first exceed 1,500,000 in 2031.11.S(t) 78.7e 0.0809terror60t Actual data S(t) 78.7e 0.0809t Absolute0 80 78.7 1.3t Actual data P(t) 232,506e 0.0264t Absolute error501 72 72.6 0.6402 66 66.9 0.9303 61 61.7 0.74 58 56.9 1.12010Largest absolute error: 1.3Sum of the absolute errors: 4.6Month1 2 3 4 5 6The sales for month 6 will be approximately $48,400.The sales will reach $20,000 in month 17.Approximately 66 rabbits (Answers may vary.)13. p(t) 9.2e 0.5142t3. P(t) 20e 0.1823tt Actual data P(t) 20e 0.1823tt Actual data p(t) 9.2e 0.5142t Absolute errorAbsolute error0 8 9.2 1.20 20 20.0 0.01 19 15.4 3.61 24 24.0 0.02 26 25.7 0.32 30 28.8 1.23 40 43.0 3.03 36 34.6 1.44 45 41.5 3.5Largest absolute error: 3.65 54 49.8 4.2Sum of the absolute errors: 8.190% will have encountered the virus approximately halfway throughLargest absolute error: 4.2the 4th quarter.Sum of the absolute errors: 10.3About 5.74 10 12 %5. P(t) 20e 0.1987t15. N(t) 2.7e 0.3226tt Actual data P(t) 20e 0.1987t Absolute errort Actual data N(t) 2.7e 0.3226t Absolute error0 20 20 00 2 2.7 0.71 24 24.4 0.43 6 7.1 1.12 30 29.8 0.27 29 25.8 3.23 36 36.3 0.311 134 93.9 40.14 45 44.3 0.714 275 247.1 27.95 54 54 018 1200 897.9 302.1Largest absolute error: 0.7Sum of the absolute errors: 1.6This model is more accurate.2226283100750024,0003,263.211,859.122,607.8163.24359.11392.27. P(t) 19.9e 0.201t30 42,000 43,098.9 1098.9t Actual data P(t) 19.9e 0.201t Absolute errorLargest absolute error: 4359.1Sum of the absolute errors: 7388.50 20 19.9 0.1There will be approximately 156,632 thousand (156,632,000)1 24 24.3 0.3transistors in 2005.2 30 29.7 0.3The number of transistors will exceed 100 billion in 2046.3 36 36.4 0.417. a. 4 students4 45 44.5 0.5b. Approximately 77 students5 54 54.4 0.4c. Approximately 17 hoursLargest absolute error: 0.5Sum of the absolute errors: 2.0The largest error is smaller, but the sum of the errors is larger.Both models are extremely accurate.d. 22009. P(t) 232,506e 0.0264t0 226,000 232,506 650610 303,000 302,753 247-24020 402,000 394,223 777730 550,000 513,329 36,67140 627,000 668,420 41,420-100Approximately 2000 studentse. The 21st hour19. a. 1945b. 700 miles per hourc. No; the model predicts 674.37 miles per hour for 1997 and hasan upper bound of 700 miles per hour.

Answers Chapter 4 Review A-2721.Largest absolute error: 0.07Sum of the absolute errors: 0.22Little Rock: 4.6 feet/secondNew York: 5.9 feet/secondMexico City: 6.2 feet/second23. False 25. TrueChapter 4 Review, page 3601.v 0.81log P 0.3P Actual data v 0.81log P 0.3 Absolute error5,500 3.3 3.33 0.0314,000 3.7 3.66 0.0471,000 4.3 4.23 0.07138,000 4.4 4.46 0.06342,000 4.8 4.78 0.02a.b.c.54321–2–3–4–5g(x) = 2 –xy54321–2–3–4–554321–2–3–4–554321–5–4–3 –2 –1 1 2 3 4 5–2–3–4–5yy–5–4–3 –2 –1 1 2 3 4 5yf(x) = 2 x–5–4–3 –2 –1 1 2 3 4 5–5–4–3 –2 –1 1 2 3 4 5xg(x) = 2 x + 2xxg(x) = 2 x + 1 x13. x 3 5. x 1 7. 2 9. 2 11.2213. 2 4 1 15. 10 4 2x 1 17. ln x 51619. log 2 5 x 321.yDomain: (0, )23.yx 2Domain: (2, )25. 227. 29. log(x 2 y 3 )3 log x 1 2 x 2log 2 y3 log y331. xy ln 10(33. 35. x 1 z)ln 4 1.66096237. x 3 39. y 12541.43.ln 10ln 10x 45. t ln 5 1.43068 ln 1.05 47.1936347. x 10 ln 5 16.09438 2 ln 349. x 2 ln 2 ln 3 7.6376851. x 2.82, x 1.66 53. x 0.17, x 5.05,55. a.x 45.48( 2 b. x 3) x ln 2ln(2/3) 1.7095157. a. x 2, x 1 b. x 2,x 159. a.6-654321–5–4–3 –2 –1 1 2 3 4 5–2–3–4–554321–5–4–3 –2 –1 1 2 3 4 5–2–3–4–5b. One solution-6( 3 2 , )61. a. x 3 2b.63. a. u 1 b. x 0f(x) = log 5 xf(x) = ln(x – 2)xx6

A-28 Answers Chapter 4 Test65. a.619.y-6b. (0, 4)67. $56.34 69. Approximately 23.1 years71. Approximately 12.6 hours73. a. Approximately 149 astronautsb. Approximately 28.8 daysc. 210,00075.-6-10-10,000Approximately 200,000 astronautsd. The 96th dayV(t) 27,957e 0.1495tLargest absolute error: 75Sum of the absolute errors: 265The SUV will be worth $4000 in 13 years.Chapter 4 Test, page 3631. False 2. True 3. False4. False 5. True 6. True1807. False 8. True 9. f(t) e t , for example10. 1, for example 11. 0.1, for example12. Limited food, for example13. x 2,x 114.15.x 10 12 1 999,999,999,999ln 3x ln 3 ln 2 2.7095116. x ln 20.3 2.3104917. 5 18. 320.21.V(t) 27,957e 0.1495t N(t) 2243e 0.6115t 5432f(x) = ln(x + 3)1x–5–4–3 –2 –1 1 2 3 4 5–2–3–4–526.22. 23. ln( x 3 z4log x 2log y 2log z10y 424. Approximately 8.8 years 25. 2029t Actual data Absolute errort Actual data Absolute error0 28,000 27,957 431 24,000 24,075 752 20,800 20,732 683 17,800 17,853 534 15,400 15,374 26654321–5–4–3 –2 –1 1 2 3 4 5–2–3–4–554321–5–4–3 –2 –1 1 2 3 4 5–2–3–4–5yyg(x) = 2 3f(x) = e x – 2x( ) x xN(t) 2243e 0.6115t0 2,100 2,243 1431 4,400 4,134 2662 8,200 7,620 5803 13,100 14,046 946Largest absolute error: 946Sum of the absolute errors: 1935Approximately 25,900 new cases in 1987The approximation overestimates the number of new cases byalmost 5000.The model predicts approximately 250 million in 2002, which is anenormous overestimate.