The population p ( t ) at a time t of a certain mouse species satisfies the differential equation dp t dt = 0.5 p ( t ) - 450 . If p ( 0 ) = 850 , then the time at which the population becomes zero is

Question

The population p ( t ) at a time t of a certain mouse species satisfies the differential equation dp t dt = 0.5 p ( t ) - 450 . If p ( 0 ) = 850 , then the time at which the population becomes zero is, 1 2 ln 18, ln 18, 2 ln 18, ln 9

MARKS App · Accepted Answer

Let, p = p ( t ) dp dt = 0.5 p - 450 = p - 9 0 0 2 ⇒ ∫ 8 5 0 p 2 p - 9 0 0 dp = ∫ 0 t dt ⇒ 2 log p - 9 0 0 850 p = t ⇒ 2 log p - 900 - log - 50 = t ⇒ 2 log p - 900 - 5 0 = t ...(1) ⇒ | p - 900 - 5 0 | = e t/2 ⇒ p = 9 0 0 - 5 0 e t/2 Let, when t = T , p = 0 (using (1)) ⇒ T = 2 ln ⁡ 18

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