Let the population of rabbits surviving at a time t be governed by the differential…

Mathematics · JEE Main · NTA ExamsDifferential Equations

Let the population of rabbits surviving at a time t be governed by the differential equation \(\frac{d p(t)}{d t}=\frac{1}{2} p(t)-200\). If \(P(0)=100\), then \(P(t)\) equals :
  1. \(600-500 \mathrm{e}^{\mathrm{t} / 2}\)
  2. \(400-300 e^{-t / 2}\)
  3. \(400-300 \mathrm{e}^{\mathrm{t} / 2}\)
  4. \(300-200 e^{-t / 2}\)

Answer

(C) 400-300 e ^ t / 2

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