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# Let the population of rabbits surviving at

Question:

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

1. $400-300 \mathrm{e}^{\mathrm{t} / 2}$

2. $300-200 \mathrm{e}^{-1 / 2}$

3. $600-500 \mathrm{e}^{\mathrm{t} / 2}$

4. $400-300 \mathrm{e}^{-1 / 2}$

Correct Option: 1

Solution: