JEE Math Practice Question
Let the population of rabbits surviving at time $$t$$ be governed by the differential equation $${{dp\left( t \right)} \over {dt}} = {1 \over 2}p\left( t \right) - 200.$$ If $$p(0)=100,$$ then $$p(t)$$ equals:
- A.$$600 - 500\,{e^{t/2}}$$
- B.$$400 - 300\,{e^{-t/2}}$$
- C.$$400 - 300\,{e^{t/2}}$$
- D.$$300 - 200\,{e^{-t/2}}$$
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