JEE-Mains 2014 (17/30)

Calculus Level 3

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

600 − 500 e t 2 600-500e^{\frac{t}{2}} 400 − 300 e t 2 400-300e^{\frac{t}{2}} 300 − 200 e − t 2 300-200e^{\frac{-t}{2}} 400 − 300 e − t 2 400-300e^{\frac{-t}{2}}

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Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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