The population p ( t ) at 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

Step-by-step solution

d(p(t)) d t = 1 2 p(t)-450 d(p(t)) d t = p(t)-900 2 2 d(p(t)) p(t)-900 = d t2 |p(t)-900|=t+ct=0 2 50=0+c c=2 50 2 | p ( t )-900|= t +2 50P( t )=0 2 900= t +2 50t=2( 900- 50)=2 ( 900 50 )=2 18 .