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JEE Main 2021 · 24 Feb · Shift 1, Mathematics question 72

The population P = P(t) at time 't' of a certain species follows the differential equation dPdt=0.5P−450\dfrac{dP}{dt}=0.5P-450. If P(0) = 850, then the time at which population becomes zero is :

Choose one option
Answer and worked solution

Official answer: D

Solve. P−900=(850−900)et/2=−50et/2P-900=(850-900)e^{t/2}=-50e^{t/2}; P = 0 when et/2=18e^{t/2}=18, t=2log⁡e18t=2\log_e18.

(D)

Topics:Variable separableFormation and applications
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