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Pre-Calc Homework Solutions 288

# Pre-Calc Homework Solutions 288 - 8 C 61 v k m 5 coasting...

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56. Method 1–Compare graph of y 1 5 x 2 ln x with y 2 5 NDER 1 } x 3 3 ln x } 2 } x 9 3 } 2 . The graphs should be the same. Method 2–Compare graph of y 1 5 NINT( x 2 ln x ) with y 2 5 } x 3 3 ln x } 2 } x 9 3 } . The graphs should be the same or differ only by a vertical translation. 57. (a) 20,000 5 10,000(1.063) t 2 5 1.063 t ln 2 5 t ln 1.063 t 5 } ln l 1 n .0 2 63 } < 11.345 It will take about 11.3 years. (b) 20,000 5 10,000 e 0.063 t 2 5 e 0.063 t ln 2 5 0.063 t t 5 } 0 l . n 06 2 3 } < 11.002 It will take about 11.0 years. 58. (a) f 9 ( x ) 5 } d d x } E x 0 u ( t ) dt 5 u ( x ) g 9 ( x ) 5 } d d x } E x 3 u ( t ) dt 5 u ( x ) (b) C 5 f ( x ) 2 g ( x ) 5 E x 0 u ( t ) dt 2 E x 3 u ( t ) dt 5 E x 0 u ( t ) dt 1 E 3 x u ( t ) dt 5 E 3 0 u ( t ) dt 59. (a) y 5 } 1 1 5 5 .8 6 9 .0 4 7 e 1 2 6 0.0205 x } [ 2 20, 200] by [ 2 10, 60] (b) The carrying capacity is about 56.0716 million people. (c) Use NDER twice to solve y 0 5 0. The solution is x < 86.52, representing (approximately) the year 1887. The population at this time was approximately P (86.52) < 28.0 million people. 60. (a) T 5 79.961(0.9273) t [ 2 1, 33] by [ 2 5, 90] (b) Solving T ( t ) 5 40 graphically, we obtain t < 9.2 sec. The temperature will reach 40 8 after about 9.2 seconds. (c) When the probe was removed, the temperature was about T (0) < 79.96 8 C. 61. } v
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Unformatted text preview: 8 C. 61. } v k m } 5 coasting distance } (0.86)( k 30.84) }5 0.97 k < 27.343 s ( t ) 5 } v k m } (1 2 e 2 ( k / m ) t ) s ( t ) 5 0.97(1 2 e 2 (27.343/30.84) t ) s ( t ) 5 0.97(1 2 e 2 0.8866 t ) A graph of the model is shown superimposed on a graph of the data. [0, 3] by [0,1] Chapter 7 Applications of Definite Integrals ■ Section 7.1 Integral as Net Change (pp. 363–374) Exploration 1 Revisiting Example 2 1. s ( t ) 5 E 1 t 2 2 } ( t 1 8 1) 2 } 2 dt 5 } t 3 3 } 1 } t 1 8 1 } 1 C s (0) 5 } 3 3 } 1 } 1 8 1 } 1 C 5 9 ⇒ C 5 1 Thus, s ( t ) 5 } t 3 3 } 1 } t 1 8 1 } 1 1. 2. s (1) 5 } 1 3 3 } 1 } 1 1 8 1 } 1 1 5 } 1 3 6 } . This is the same as the answer we found in Example 2a. 3. s (5) 5 } 5 3 3 } 1 } 5 1 8 1 } 1 1 5 44. This is the same answer we found in Example 2b. 288 Section 7.1...
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