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(b) The given graph is reflected about the x -axis. (c) The given graph is shifted left 1 unit, stretched vertically by a factor of 2, reflected about the x -axis, and then shifted upward 1 unit. (d) The given graph is shifted right 2 units, stretched vertically by a factor of 3, and then shifted downward 2 units. 61. (a) (b) 62. (a) V 5 100,000 2 10,000 x, 0 # x # 10 (b) V 5 55,000 100,000 2 10,000 x 5 55,000 2 10,000 x 5 2 45,000 x 5 4.5 The value is \$55,000 after 4.5 years. 63. (a) f (0) 5 90 units (b) f (2) 5 90 2 52 ln 3 < 32.8722 units (c) [0, 4] by [ 2 20, 100] 64. 1500(1.08) t 5 5000 1.08 t 5 } 5 1 0 5 0 0 0 0 } 5 } 1 3 0 } ln (1.08) t 5 ln } 1 3 0 } t ln 1.08 5 ln } 1 3 0 } t 5 } ln ln (1 1 0 .0 / 8 3) } t < 15.6439 It will take about 15.6439 years. (If the bank only pays interest at the end of the year, it will take 16 years.) 65. (a) N ( t ) 5 4 ? 2 t (b) 4 days: 4 ? 2 4 5 64 guppies 1 week: 4 ? 2 7 5 512 guppies (c) N ( t ) 5 2000 4 ? 2 t 5 2000 2 t 5 500 ln 2 t 5 ln 500 t ln 2 5 ln 500 t 5 } ln ln 50 2 0 } < 8.9658 There will be 2000 guppies after 8.9658 days, or after nearly 9 days. (d) Because it suggests the number of guppies will continue to double indefinitely and become arbitrarily large, which is impossible due to the finite size of the tank and the oxygen supply in the water. 66. (a) y 5 20.627 x 1 338.622 [0, 30] by [ 2 100, 1000] (b) When x 5 30, y < 957.445. According to the regression equation, about 957 degrees will be earned. (c) The slope is 20.627. It represents the approximate annual increase in the number of doctorates earned by Hispanic Americans per year. 67. (a) y 5 14.60175 ? 1.00232 x (b) Solving y 5 25 graphically, we obtain x < 232. According to the regression equation, the population will reach 25 million in the year 2132. (c) 0.232% y x 3 –3 –3 3 (–3, –2) (–1, 1) (1, –1) (3, 2) y x 3 3 –3 –3 (–3, 2) (–1, –1) (1, –1) (3, 2) y x 4 –2 4 (–1, –2) (2, 4) (3, –2) y = 3 f ( x – 2) – 2 y x 3 2 –4 (–4, 1) (–1, –3) (0, 1) y = –2 f ( x + 1) + 1 y x 3 –3 –3 3 (–3, 0) (0, –2) (1, 0) y = – f ( x ) Chapter 1 Review 41

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Chapter 2 Limits and Continuity Section 2.1 Rates of Change and Limits (pp. 55–65) Quick Review 2.1 1. f (2) 5 2(2 3 ) 2 5(2) 2 1 4 5 0 2. f (2) 5 } 4( 2 2 3 ) 2 1 2 4 5 } 5 } 1 1 1 2 } 3. f (2) 5 sin 1 p ? } 2 2 } 2 5 sin p 5 0 4. f (2) 5 } 2 2 1 2 1 } 5 } 1 3 } 5. ) x ) , 4 2 4 , x , 4 6. ) x ) , c 2 2 c 2 , x , c 2 7. ) x 2 2 ) , 3 2 3 , x 2 2 , 3 2 1 , x , 5 8. ) x 2 c ) , d 2 2 d 2 , x 2 c , d 2 2 d 2 1 c , x , d 2 1 c 9.
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