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Pre-Calc Homework Solutions 263

Pre-Calc Homework Solutions 263 - 8 C 35(a d d T t 5 2 k T...

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30. (a) A ( t ) 5 A 0 e t It grows by a factor of e each year. (b) 3 5 e t ln 3 5 t It will take ln 3 < 1.1 yr. (c) In one year your account grows from A 0 to A 0 e , so you can earn A 0 e 2 A 0 , or ( e 2 1) times your initial amount. This represents an increase of about 172%. 31. (a) s ( t ) 5 E v 0 e 2 ( k / m ) t dt 5 2 } v 0 k m } e 2 ( k / m ) t 1 C Initial condition: s (0) 5 0 0 5 2 } v 0 k m } 1 C } v 0 k m } 5 C s ( t ) 5 2 } v 0 k m } e 2 ( k / m ) t 1 } v 0 k m } 5 } v 0 k m } 1 1 2 e 2 ( k / m ) t 2 (b) lim t s ( t ) 5 lim t } v 0 k m } 1 1 2 e 2 ( k / m ) t 2 5 } v 0 k m } 32. (a) 90 5 e ( r )(100) ln 90 5 100 r r 5 } l 1 n 0 9 0 0 } < 0.045 or 4.5% (b) 131 5 e ( r )(100) ln 131 5 100 r r 5 } ln 10 1 0 31 } < 0.049 or 4.9% 33. } v 0 k m } 5 coasting distance } (0.80)( k 49.90) } 5 1.32 k 5 } 9 3 9 3 8 } We know that } v 0 k m } 5 1.32 and } m k } 5 } 33 9 (4 9 9 8 .9) } 5 } 2 3 0 3 } . Using Equation 3, we have: s ( t ) 5 } v 0 k m } (1 2 e 2 ( k / m ) t ) 5 1.32(1 2 e 2 20 t /33 ) < 1.32(1 2 e 2 0.606 t ) A graph of the model is shown superimposed on a graph of the data. [0, 4.7] by [0, 1.4] 34. (a) T 2 T s 5 79.47(0.932) t (b) T 5 10 1 79.47(0.932) t [0, 35] by [0, 90] (c) Solving T 5 12 and using the exact values from the regression equation, we obtain t < 52.5 sec. (d) Substituting t 5 0 into the equation we found in part (b), the temperature was approximately 89.47
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Unformatted text preview: 8 C. 35. (a) } d d T t } 5 2 k ( T 2 T s ) } T 2 dT T s }5 2 k dt E } T 2 dT T s }5 2 k dt ln ) T 2 T s ) 5 2 kt 1 C ) T 2 T s ) 5 e 2 kt 1 C T 2 T s 5 6 e C e 2 kt T 2 T s 5 Ae 2 kt Initial condition: T 5 T when t 5 T 2 T s 5 Ae 2 ( k )(0) T 2 T s 5 A Solution: T 2 T s 5 ( T 2 T s ) e 2 kt (b) lim t → ‘ T 5 lim t → ‘ [ T s 1 ( T 2 T s ) e 2 kt ] 5 T s Horizontal asymptote: T 5 T s 36. (a) 2 y 5 y e rt 2 5 e rt ln 2 5 rt t 5 } ln r 2 } (b) [0, 0.1] by [0, 100] (c) ln 2 < 0.69, so the doubling time is } 0. r 69 } which is almost the same as the rules. (d) } 7 5 } 5 14 years or } 7 5 2 } = 14.4 years Section 6.4 263...
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