InterviewSolution
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InterviewSolution
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Let thepopulation of rabbits surviving at a time t be governed by the differentialequation `(d p(t)/(dt)=1/2p(t)-200.`If `p(0)""=""100`, then p(t) equals(1) `400-300""e^(t//2)`(2) `300-200""e^(-t//2)`(3) `600-500""e^(t//2)`(4) `400-300""e^(-t//2)`A. (a) `400-300e^(t/2)`B. (b) `300-200e^(t/2)`C. (c) `600-500e^(t/2)`D. (d) `400-300e^(t/2)` |
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Answer» Correct Answer - (a) Given, differential equation is `(dp)/dt-1/2p(t)=-200` a linear differential equation. Here, `p(t)=(-1)/2,Q(t)=-200` `IF=e^(int-(1/2)dt)=e^(t/2)` Hence, solution is `p(t) cdot IF = int Q(t) cdot IF dt` `p(t) cdot e^(t/2)=int-200 cdot e ^(t/2)dt` `p(t) cdot e^(t/2)=400 cdot e ^(t/2)+k` `rArr p(t)=400 +ke^(-1//2)` If p(0)=100, then k=-300 `rArr p(t)=400-300e^(1/2)` |
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