# Let the population of rabbits surviving at a time $'t'$ be governed by the differential equation $\large\frac{dp(t)}{dt}=\frac{1}{2}$$p(t)-200$ <br> If p(0)= 100, then what is the value of p(t)?
$\begin{array}{1 1}(A)\;400-300e^{\Large\frac{t}{2}}\\(B)\;300-200e^{\Large\frac{-t}{2}}\\(C)\;600-500e^{\Large\frac{t}{2}}\\(D)\;400-300e^{\Large\frac{-t}{2}}\end{array}$