Differential Equations · JEE Main previous year questions

2014 1 question

1. Q162014 · 6 Apr 2014 · Shift 1

   Let the population of rabbits surviving at time $t$ be governed by the differential equation $\frac{dp(t)}{dt}=\frac{1}{2}p(t)-200$. If $p(0)=100$, then $p(t)$ equals:

   1. A.$600-500e^{t/2}$
   2. B.$400-300e^{-t/2}$
   3. C.$400-300e^{t/2}$
   4. D.$300-200e^{-t/2}$
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   Answer: C