Pre-Calc Homework Solutions 270

Pre-Calc Homework Solutions 270 - 270 Section 6.5 0, x 20,...

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23. (a) Note that the given years correspond to x 5 0, x 5 20, x 5 50, x 5 70, and x 5 80. y 5 } 1 1 1.0 1 7 8 5 .7 e 0 2 0.0422 x } [0, 100] by [0, 20] (b) Carrying capacity 5 lim x y 5 18.70, representing 18.7 million people. (c) Using NDER twice and solving graphically, we find that y 05 0 when x < 1.7, corresponding to the year 1912. The population at this time was about y (1.7) < 9.35 million. 24. (a) y 5 } 1 1 7.1 2 9 4 5 .7 e 6 2 0.0513 x } [0, 50] by [0, 15] (b) Carrying capacity 5 lim x y 5 24.76, representing 24.76 million people. (c) Using NDER twice and solving graphically, we find that y 0 when x < 38.44, corresponding to the year 1988. The population at this time was about y (38.44) < 12.38 million. 25. } d d P t } 5 } M k } P ( M 2 P ) } P ( M M d 2 P P ) } 5 k dt } ( M P ( 2 M P 2 ) 1 P ) P } dP 5 k dt 1 } P 1 } 1 } M 2 1 P } 2 dP 5 k dt ln ) P ) 2 ln ) M 2 P ) 5 kt 1 C ln ) } M P 2 P } ) 5 kt 1 C ln ) } M 2 P P } ) 52 kt 2 C } M 2 P P }56 e 2 C e 2 kt } M 2 P P } 5 Ae 2 kt M 2 P 5 APe 2 kt M 5 P (1 1 Ae 2 kt ) P 5 } 1 1 M Ae 2 kt } 26. (a) y 5 } 1 1 5.1 1 3 6 2 .9 e 0 2 0.0666 x } (b) Carrying capacity 5 lim x y 5 16.90 representing 16.9 million people. 27. } d d y x } 5 (cos x ) e sin x E dy 5 E (cos x ) e sin
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