The population P = P t at time t of a certain species follows the differential equation d P d t = 0 . 5 P - 450 . If P 0 = 850 , then the time at which population becomes zero is:

Question

The population P = P t at time t of a certain species follows the differential equation d P d t = 0 . 5 P - 450 . If P 0 = 850 , then the time at which population becomes zero is:, log e 9, 2 log e 18, log e 18, 1 2 log e 18

MARKS App · Accepted Answer

d P d t = 0 . 5 P - 450 ⇒ ∫ 0 t d p P - 900 = ∫ 0 t d t 2 ⇒ In P t - 900 0 t = t 2 0 t ⇒ In P t - 900 - In P 0 - 900 = t 2 ⇒ In P t - 900 - In 50 = t 2 for P t = 0 ⇒ In 900 50 = t 2 ⇒ t = 2 In 18

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