The population P = P(t) at time ‘t’ of a certain species follows the differential equationdPdt=0.5P−450 . If P0=850then the time at which population becomes zero is:

The given differential equation dPtdt=Pt−9002integrate both sides ∫0tdPtPt−900=∫0tdt2lnPt−9000t=t20tlnPt−900−lnP0−900=t2lnPt−900−ln50=t2When population becomes zeroit gives ln900−ln50=t2t=2ln90050=2ln18therefore, t=2ln18