The population P = P t at time t of a certain species follows the differential equation d P d t = 0 . 5 P -…

The population P=Pt at time t of a certain species follows the differential equation dPdt=0.5P-450. If P0=850, then the time at which population becomes zero is:
  1. loge9
  2. 2loge18
  3. loge18
  4. 12loge18

Solution

dPdt=0.5P-450

⇒  ∫0tdpP-900=∫0tdt2

⇒  InPt-9000t=t20t

⇒  InPt-900-InP0-900=t2

⇒  InPt-900-In50=t2

for Pt=0

⇒ In90050=t2⇒t=2In18

Asked in: JEE Main 2021 (24 Feb Shift 1)

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