JEE Main 2014Session, Shift 1MathematicsMediumDifferential Equations163× since 2002Let the population of rabbits surviving at time ttt be governed by the differential equation dp(t)dt=12p(t)−200.{{dp\left( t \right)} \over {dt}} = {1 \over 2}p\left( t \right) - 200.dtdp(t)=21p(t)−200. If p(0)=100,p(0)=100,p(0)=100, then p(t)p(t)p(t) equals:AOption A. 600−500 et/2600 - 500\,{e^{t/2}}600−500et/2BOption B. 400−300 e−t/2400 - 300\,{e^{-t/2}}400−300e−t/2COption C. 400−300 et/2400 - 300\,{e^{t/2}}400−300et/2DOption D. 300−200 e−t/2300 - 200\,{e^{-t/2}}300−200e−t/2CheckSkip · show solution
