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Differential Equations question

2014 · Shift 0 · Q27
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  5. /2014 · Shift 0 · Q27

Differential Equations question

2014 · Shift 0 · Q27

JEE MainMathematicsDifferential EquationsMCQ+4 / −1
Let 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)​=21​p(t)−200. If p(0)=100,p(0)=100,p(0)=100, then p(t)p(t)p(t) equals:
  1. A
    600−500 et/2600 - 500\,{e^{t/2}}600−500et/2
  2. B
    400−300 e−t/2400 - 300\,{e^{-t/2}}400−300e−t/2
  3. C
    400−300 et/2400 - 300\,{e^{t/2}}400−300et/2
  4. D
    300−200 e−t/2300 - 200\,{e^{-t/2}}300−200e−t/2
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