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Pre-Calc Homework Solutions 268

# Pre-Calc Homework Solutions 268 - 5 1 1 A 1 e 5 2 0.225 t...

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13. (a) P ( t ) 5 } 1 1 1 e 0 4 0 .8 0 2 0.7 t } 5 } 1 1 1 e 0 4. 0 8 e 0 2 0.7 t } 5 } 1 1 M Ae 2 kt } This is a logistic growth model with k 5 0.7 and M 5 1000. (b) P (0) 5 } 1 1 1 00 e 0 4.8 } < 8 Initially there are 8 rabbits. 14. (a) P ( t ) 5 } 1 1 20 e 0 5.3 2 t } 5 } 1 1 2 e 0 5 0 .3 e 2 t } 5 } 1 1 M Ae 2 kt } This is a logistic growth model with k 5 1 and M 5 200. (b) P (0) 5 } 1 1 20 e 0 5.3 } < 1 Initially 1 student has the measles. 15. (a) Note that } d d P T } 5 } 1 1 p 4 er s s e o c n } ? < 2,252,571 people per year. The relative growth rate is < } 2 2 5 , 7 2 , 5 3 2 1 , 3 5 , 7 4 1 31 } < 0.00875 or 0.875% (b) The population after 8 years will be approximately P 0 e rt 5 257,313,431 e 8 r < 275,980,017, where r is the unrounded rate from part (a). 16. (a) Let t be the number of years. 1000 5 10,000(0.8) t 0.1 5 0.8 t ln 0.1 5 t ln 0.8 t 5 } l l n n 0 0 . . 1 8 } < 10.32 It will take about 10.32 years. (b) Let f ( t ) 5 10,000(0.8) t . So that f ( t ) will round to less than 1, we actually require f ( t ) , 0.5. 0.5 5 10,000(0.8) t 0.00005 5 0.8 t ln 0.00005 5 t ln 0.8 t 5 } ln l 0 n .0 0 0 . 0 8 05 } < 44.38 It will take about 44.4 years. 17. (a) } d d P t } 5 0.0015 P (150 2 P ) 5 } 0 1 .2 5 2 0 5 } P (150 2 P ) 5 } M k } P ( M 2 P ) Thus, k 5 0.225 and M 5 150. P 5 } 1 1 M Ae 2 kt } 5 } 1 1 A
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Unformatted text preview: 5 } 1 1 A 1 e 5 2 0.225 t } Initial condition: P (0) 5 6 6 5 } 1 1 15 A e } 1 1 A 5 25 A 5 24 Formula: P 5 } 1 1 2 1 4 5 e 2 0.225 t } (b) 100 5 } 1 1 2 1 4 5 e 2 0.225 t } 1 1 24 e 2 0.225 t 5 } 3 2 } 24 e 2 0.225 t 5 } 1 2 } e 2 0.225 t 5 } 4 1 8 } 2 0.225 t 5 2 ln 48 t 5 } ln .2 4 2 8 5 } < 17.21 weeks 125 5 } 1 1 2 1 4 5 e 2 0.225 t } 1 1 24 e 2 0.225 t 5 } 6 5 } 24 e 2 0.225 t 5 } 1 5 } e 2 0.225 t 5 } 1 1 20 } 2 0.225 t 5 2 ln 120 t 5 } l n .2 1 2 2 5 } < 21.28 It will take about 17.21 weeks to reach 100 guppies, and about 21.28 weeks to reach 125 guppies. } d d P T } } P 365 ? 24 ? 3600 sec }} 1 yr 268 Section 6.5...
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