The population P = P ( t ) at time t of certain species follows the differential equation dP dt =0.5 P -450 . If P (0)=850 , then the time at which population becomes zero is

Step-by-step solution

Given differential equation is aligned & dP dt =0.5 P -450 & = P 2 - 900 2 & dP dt = P -900 2 & 2 dP P -900 = dt & Integrating on both sides, we get & 2 | P -900|= t + c & P (0)=850 i.e., P =850 when t =0 & c =2 50 & 2 | P -900|= t +2 50 & When P =0, & 2 900= t +2 50 & t =2( 900- 50) & =2 900 50 =2 18 aligned