Section 5.8 AN41 5.7 Assess Your Understanding (page 351) 3. principal 4. I; Prt; simple interest 5. effective rate of interest 6. a 7. $108.29 9. $969.56 11. $1394.19 13. $1246.08 15. $88.72 17. $1444.79 19. $713.53 21. $102.00 23. 5.095% 25. 4.081% 27. 6 1 4 % compounded annually 29. 9% compounded monthly 31. 25.992% 33. 24.573% 35. (a) About 8.69 yr (b) About 8.66 yr 37. 6.823% 39. 10.15 yr; 10.14 yr 41. 15.27 yr or 15 yr, 3 mo 43. $104,335 45. $12,910.62 47. About $30.17 per share or $3017 49. Not quite. Jim will have $1057.60. The second bank gives a better deal, since Jim will have $1060.62 after 1 yr. 51. Will has $11,632.73; Henry has $10,947.89. 53. (a) $91,019 (b) $63,502 55. 64.9 yr 57. $942.60 59. 2.6% 61. 35.003 yr 63. (a) $3686.45 (b) $3678.79 65. $6439.28 67. (a) 11.90 yr (b) 22.11 yr (c) mP P r n m r n m r n nt r n t m n r n 1 1 ln ln 1 ln 1 ln ln 1 nt nt nt ( ) ( ) ( ) ( ) ( ) = + = + = + = + = + 69. (a) 1.51% (b) In 2030 or after 17 yr 71. 22.7 yr 76. R 0; = yes 77. f x x x 2 1 1( ) = − − 78. f x x x x 2, 5; 2 5 1 2 2 ( ) ( ) ( ) ( ) − = + − + 79. 6{ } 80. x x x x 2 3 5 5 ( )( ) ( ) + − + 81. f g x x x 45 18 7 2 ( )( ) = − − 82. Domain: , ; ( ) −∞ ∞ Range: , 9 ( ) −∞ 83. Vertical: x 7; = horizontal: none; oblique: y x2 9 = + 84. y x4 18 = − 85. 3 111. (a) 2054 (b) 2072 113. (a) After 2.4 yr (b) After 3.8 yr (c) After 9.4 yr 115. (a) 2.24 (b) 2.15 (c) $887.93 (d) $0.03 (e) $25.70; 2.18 (f) For experts, as the price increases, the wine rating also increases. For nonexperts, as the price increases, the wine rating decreases. 117. 3log3 { } 120. 3, 1 4 , 2 { } − 121. one-to-one 122. f g x x x x x x 5 11 ; 3, 11 ( )( ) { } = + − + ≠ ≠ 123. x x 1 or 1, { } [ ) ≥ ∞ 124. 9{ } 125. 6 126. x x x x 7 10 2 2 2 ( )( ) + − − + 127. 4 10 128. 1 6 129. x x 1 6 + + 43. 1 9 , 243 { } 45. 8{ } 47. { } { } = log 10 1 log2 2 49. log 1.2 ln 1.2 ln 8 8 { } { } − = − 51. 1 3 log 8 5 ln 8 5 3ln2 2 { } = ⎧ ⎨ ⎪⎪⎪ ⎩ ⎪⎪⎪ ⎫ ⎬ ⎪⎪⎪ ⎭ ⎪⎪⎪ 53. ln 3 2 ln 3 ln 4 { } + 55. ln 7 ln 0.6 ln 7 { } + 57. 0{ } 59. ln 1 ln π π { } + 61. ln 3 ln 2 { } 63. 0{ } 65. log 2 7 4( ) { } − + 67. log 45 { } 69. No real solution 71. log 54 { } 73. 2.79 { } 75. 0.57 { } − 77. 0.70 { } − 79. 0.57 { } 81. 0.39, 1.00 { } 83. 1.32 { } 85. 1.31 { } 87. 2, 3 { } 89. 26 8 10 9 , 26 8 10 9 5.7, 0.078 { } { } + − ≈ 91. 81 { } 93. 1, 2 3 { } − 95. 0{ } 97. ln 2 5 1.444 ( ) { } { } + ≈ 99. { } { } ≈ e 1.921 ln5 ln3 ln15 101. (a) 5 ; 5, 3 { } ( ) (b) 5 ; 5, 4 { } ( ) (c) 1 ; { } yes, at 1, 2 ( ) (d) 5{ } (e) 1 11 { } − 103. (a), (b) y 18 x 2.5 (0.710, 6.541) f(x) 5 3x 1 1 g(x) 5 2x 1 2 (c) x x 0.710 or 0.710, { } ( ) > ∞ 105. (a), (b), (c) y 18 x 3 f(x) 5 3x g(x) 5 10 (log 3 10, 10) 107. (a), (b), (c) y x 5 5 1 2 , 2Ï2 f(x) 5 2x 1 1 g(x) 5 22x 1 2 109. (a) y x 5 5 f(x) 5 2x 2 4 y 5 24 (b) 2 (c) x x 2 or , 2 { } ( ) < −∞ 5.8 Assess Your Understanding (page 363) 1. (a) 500 insects (b) 0.02 2% = per day (c) 2500 0 0 80 (d) About 611 insects (e) After about 23.5 days (f) After about 34.7 days 11. (a) 9953 years ago (b) 1 0 0 30,000 (c) 5730 yr 13. (a) 5:18 pm (b) 450 0 0 60 (c) About 14.3 min (d) The temperature of the pizza approaches 70 F° . 15. (a) 18.63 C; 25.07 C ° ° (b) 35 0 0 50 17. 1.7 ppm; 7.17 days, or 172 h 19. 0.26 M; 6.58 h, or 395 min 21. 26.6 days 3. (a) 0.0244 2.44% − = − per year (b) 500 0 0 100 (c) About 391.7 g (d) After about 9.1 yr (e) 28.4 yr 5. (a) N t N ekt 0 ( ) = (b) 5832 (c) 3.9 days 7. (a) N t N ekt 0 ( ) = (b) 25,198 9. 9.797 g
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