InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
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. `40-300e^(t//2)`B. `200-200e^(-t//2)`C. `600-500e^(t//2)`D. `400-300e^(-t//2)` |
|
Answer» Correct Answer - A `(dp)/(dt) = (p-400)/(2)` `rArr (dp)/(p-400)=1/2dt` Integrating, we get `"ln "|p-400|=1/2t+c` When `t=0, p=100`, we have ln 300=c `therefore "ln"|(p-400)/(300)|=t/2` `rArr |p-400|=300e^(t//2)` `rArr 400-p=300e^(t//2)` (as `p lt 400)` `rArr p=400-300e^(t//2)` |
|