JEE Main 2014 · 6 Apr · Shift 1 · Mathematics Q77

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MathematicsSingle correct+4 / -1Question 77 of 90

Let the population of rabbits surviving at a time $t$ be governed by the differential equation $\dfrac{dp(t)}{dt}=\dfrac12p(t)-200$ . If $p(0)=100$ , then $p(t)$ equals :

600-500\,e^{t/2}

400-300\,e^{-t/2}

400-300\,e^{t/2}

300-200\,e^{-t/2}

Answer and worked solution

Official answer: C

$\dfrac{dp}{dt}=\dfrac12(p-400)$ , so $p-400=(p(0)-400)e^{t/2}=-300e^{t/2}$ . Hence
$p(t)=400-300e^{t/2}.$

Topics:Linear first-order equations Formation and applications

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JEE Main 2014 · 6 Apr · Shift 1, Mathematics question 77