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$The population p(t) at time ‘t’ of a certain mouse species satisfies$
$differential equation \frac{d}{dt} p (t) = 0.5 p (t) - 450 . If P (0) = 850, then the time at which the population becomes zero is$

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Correct option is A

ddtp(t)=0.5p(t)−450 dp(t)dt=p(t)2-450 2∫dp(t)900−p(t)=−∫dt⇒−2ln⁡(900−p(t))=−t+cWhen t=0, p(0)=850 ⇒c=-ln(50)−2ln⁡(900−p(t))=−t+-ln50∴2ln⁡900-p(t)50=t When population becomes zero p(t)=02ln90050=t2ln18=t

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The population p(t) at time ‘t’ of a certain mouse species satisfies differential equation ddtp(t)=0.5p(t)−450. If P(0)=850 , then the time at which the population becomes zero is

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Ready to Test Your Skills?

free study material

$The population p(t) at time ‘t’ of a certain mouse species satisfies$
$differential equation \frac{d}{dt} p (t) = 0.5 p (t) - 450 . If P (0) = 850, then the time at which the population becomes zero is$