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

Question

$(a)\;600-500e^{\large\frac{t}{2}}\qquad(b)\;400-300e^{-\large\frac{t}{2}}\qquad(c)\;400-300e^{\large\frac{t}{2}}\qquad(d)\;300-200e^{-\large\frac{t}{2}}$