A-28 Answers to Selected Exercises 23. 9000 yr 25. 15,600 yr 27. 6.25°C 29. (a) 3% compounded quarterly (b) $826.95 31. 27.73 yr 33. 36.62 yr 35. (a) 315 members (b) 229 members (c) 142 members 37. (a) P0 = 1; a ≈1.01355 (b) 1.3 billion (c) 2030 39. (a) $1117 (b) 2013 41. (a) $2070 billion (b) $2252 billion (c) $2450 billion 43. (a) y = 14,225e0.034t (b) 2025–26 45. (a) 15,000 people (b) 9098 people (c) 5249 people 47. (a) 611 million bacteria (b) 746 million bacteria (c) 1007 million bacteria 49. 13.2 hr 51. 2024 53. 6.9 yr 55. 11.6 yr 57. (a) 0.065; 0.82; Among people age 25, 6.5% have some CHD, while among people age 65, 82% have some CHD. (b) 48 yr Summary Exercises on Functions: Domains and Defining Equations 1. 1-∞, ∞2 2. C 7 2 , ∞B 3. 1-∞, ∞2 4. 1-∞, 62 ´16, ∞2 5. 1-∞, ∞2 6. 1-∞, -34 ´33, ∞2 7. 1-∞, -32 ´1-3, 32 ´13, ∞2 8. 1-∞, ∞2 9. 1-4, 42 10. 1-∞, -72 ´13, ∞2 11. 1-∞, -14 ´38, ∞2 12. 1-∞, 02 ´10, ∞2 13. 1-∞, ∞2 14. 1-∞, -52 ´1-5, ∞2 15. 31, ∞2 16. A -∞, -25 B ´ A -25, 25 B ´ A 25, ∞B 17. 1-∞, ∞2 18. 1-∞, -12 ´1-1, 12 ´11, ∞2 19. 1-∞, 12 20. 1-∞, 22 ´12, ∞2 21. 1-∞, ∞2 22. 3-2, 34 ´34, ∞2 23. 1-∞, -22 ´1-2, 32 ´13, ∞2 24. 3-3, ∞2 25. 1-∞, 02 ´10, ∞2 26. A -∞, -27 B ´ A -27, 27 B ´ A 27, ∞B 27. 1-∞, ∞2 28. ∅ 29. 3-2, 24 30. 1-∞, ∞2 31. 1-∞, -74 ´1-4, 32 ´39, ∞2 32. 1-∞, ∞2 33. 1-∞, 54 34. 1-∞, 32 35. 1-∞, 42 ´14, ∞2 36. 1-∞, ∞2 37. 1-∞, -54 ´35, ∞2 38. 1-∞, ∞2 39. 1-2, 62 40. 10, 12 ´11, ∞2 41. A 42. B 43. C 44. D 45. A 46. B 47. D 48. C 49. C 50. B Chapter 4 Review Exercises 1. not one-to-one 3. one-to-one 5. not one-to-one 7. ƒ-11x2 = 23 x + 3 9. It represents the number of years after 2019 for the investment to reach $50,000. 11. one-to-one 13. B 15. C 17. log2 32 = 5 19. log3/4 4 3 = -1 21. 103 = 1000 23. e1/2 = 2e 25. 2 27. log3 m+ log3 n - log3 5 - log3 r 29. -1.3862 31. 11.8776 33. 1.1592 35. E22 5 F 37. 53.6676 39. 5-13.2576 41. 5-0.4856 4.5 Exercises 1. B 3. E 5. D 7. log7 19; log 19 log 7 ; ln 19 ln 7 9. log1/2 12; log 12 log 1 2 ; ln 12 ln 1 2 11. 51.7716 13. 5-2.3226 15. 5-6.2136 17. 5-1.7106 19. 53.2406 21. 5{2.1466 23. 59.3866 25. ∅ 27. 532.9506 29. 57.0446 31. 525.6776 33. 52011.5686 35. 5ln 2, ln 46 37. Eln 3 2F 39. 5log5 46 41. 5e26 43. Ee1.5 4 F 45. E2 - 210F 47. 5166 49. 536 51. 5e6 53. 5-6, 46 55. 5-8, 06 57. 556 59. 5-56 61. ∅ 63. 5-26 65. 506 67. 5126 69. 5256 71. ∅ 73. E5 2F 75. 536 77. U 1 + 241 4 V 79. 566 81. 546 83. 51, 1006 85. Proposed solutions that cause any argument of a logarithm to be negative or 0 must be rejected. The statement is not correct. For example, the solution set of log1-x + 992 = 2 is 5-16. 87. x = ek/1p-a2 89. t = - 1 k log Q T - T0 T1 - T0R 91. t = - 2 R ln A1 - RI E B 93. x = ln Q A + B - y B R -C 95. A = B xC 97. t = log A P n log A1 + r nB 99. $11,611.84 101. 2.6 yr 103. 2.64% 105. (a) 10.9% (b) 35.8% (c) 84.1% 107. (a) $23,394 (b) 2019 109. (a) 2065 thousand (b) 2015 111. (a) P1x2 = 1 - e-0.0034-0.0053x (b) P(x) = 1 − e−0.0034 − 0.0053x 0 0 1 1000 (c) P1602 ≈0.275, or 27.5%; The reduction in carbon emissions from a tax of $60 per ton of carbon is 27.5%. (d) x = $130.14 113. ƒ-11x2 = ln x + 5; domain: 10, ∞2; range: 1-∞, ∞2 115. ƒ-11x2 = ln1x + 42 - 1; domain: 1-4, ∞2; range: 1-∞, ∞2 117. ƒ-11x2 = 1 3 e x/2; domain: 1-∞, ∞2; range: 10, ∞2 119. 51.526 121. 506 123. 52.45, 5.666 125. When each side is divided by log 1 3 , the direction of the inequality symbol should be reversed because log 1 3 is negative. 4.6 Exercises 1. B 3. C 5. B 7. C 9. 1 3 ln 1 3 11. 1 100 ln 1 2 13. 1 2 ln 1 4 15. (a) 440 g (b) 387 g (c) 264 g (d) 22 yr 17. 1600 yr 19. 3.6 g 21. 16 days
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