Questions Asked in Previous 10 Years' Exams Let the population of rabbits surviving at a time \(...

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Questions Asked in Previous 10 Years' Exams
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 \( p(t) \) is equal to [2014 JEE Main]
(a) \( 400-300 e^{\frac{t}{2}} \)
(b) \( 300-200 e^{\frac{t}{2}} \)
(c) \( 600-500 e^{\frac{\ell}{2}} \)
(d) \( 400-300 e^{\frac{t}{2}} \)
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