# Business Calc Homework w answers_Part_53 - 17 At time t 5 3...

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Unformatted text preview: 17. At time t 5 } 3 k } , the amount remaining is y e 2 kt 5 y e 2 k (3/ k ) 5 y e 2 3 &amp;lt; 0.0499 y . This is less than 5% of the original amount, which means that over 95% has decayed already. 18. T 2 T s 5 ( T 2 T s ) e 2 kt 35 2 65 5 ( T 2 65) e 2 ( k )(10) 50 2 65 5 ( T 2 65) e 2 ( k )(20) Dividing the first equation by the second, we have: 2 5 e 10 k k 5 } 1 1 } ln 2 Substituting back into the first equation, we have: 2 30 5 ( T 2 65) e 2 [(ln 2)/10](10) 2 30 5 ( T 2 65) 1 } 1 2 } 2 2 60 5 T 2 65 5 5 T The beams initial temperature is 5 8 F. 19. (a) First, we find the value of k . T 2 T s 5 ( T 2 T s ) e 2 kt 60 2 20 5 (90 2 20) e 2 ( k )(10) } 4 7 } 5 e 2 10 k k 5 2} 1 1 } ln } 4 7 } When the soup cools to 35 8 , we have: 35 2 20 5 (90 2 20) e [(1/10) ln (4/7)] t 15 5 70 e [(1/10) ln (4/7)] t ln } 1 3 4 } 5 1 } 1 1 } ln } 4 7 } 2 t t 5 &amp;lt; 27.53 min It takes a total of about 27.53 minutes, which is an additional 17.53 minutes after the first 10 minutes. (b) Using the same value of k as in part (a), we have: T 2 T s 5 ( T 2 T s ) e 2 kt 35 2 ( 2 15) 5 [90 2 ( 2 15)] e [(1/10) ln (4/7)] t 50 5 105 e [(1/10) ln (4/7)] t ln } 1 2 1 } 5 1 } 1 1 } ln } 4 7 } 2 t t 5 &amp;lt; 13.26 It takes about 13.26 minutes 20. First, we find the value of k . Taking right now as t 5 0, 60 8 above room temperature means T 2 T s 5 60. Thus, we have T 2 T s 5 ( T 2 T s ) e 2 kt 70 5 60 e ( 2 k )( 2 20) } 7 6 } 5 e 20 k k 5 } 2 1 } ln } 7 6 } (a) T 2 T s 5 ( T 2 T s ) e 2 kt 5 60 e ( 2 (1/20)ln (7/6))(15) &amp;lt; 53.45 It will be about 53.45 8 C above room temperature. (b) T 2 T s 5 ( T 2 T s ) e 2 kt 5 60 e ( 2 (1/20)ln (7/6))(120) &amp;lt; 23.79 It will be about 23.79 8 above room temperature. (c) T 2 T s 5 ( T 2 T s ) e 2 kt 10 5 60 e ( 2 (1/20)ln (7/6)) t ln } 1 6 } 5 1 2} 2 1 } ln } 7 6 } 2 t t 5 2 } 20 ln ln (7 ( / 1 6 / ) 6) } &amp;lt; 232.47 min It will take about 232.47 min or 3.9 hr. 21. Use k 5 } 5 l 7 n 2 } (see Example 3). e 2 kt 5 0.445 2 kt 5 ln 0.445 t 5 2 } ln 0 k .445 } 5 2 } 5700 l l n n 2 0.445 } &amp;lt; 6658 years Crater Lake is about 6658 years old....
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Business Calc Homework w answers_Part_53 - 17 At time t 5 3...

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