The population P ( t ) of a certain mouse species at time t satisfies the differential equation d P(t) d t =0 5 P(t)-450 If P (0)=850 , then the time at which the population becomes zero is

Step-by-step solution

dp ( t ) dt =0.5 p ( t )-450 dp ( t ) dt = 1 2 p ( t )-450 dp ( t ) dt = p ( t )-900 2 2 d [ p ( t )] p ( t )-900 = dt 2 | p ( t )-900|= t + c When t =0, p ( t )=850 2 |850-900|=0+ c c =2 50 2 | p ( t )-900|= t +2 50 When p ( t )=0 , we write 2 |0-900|= t +2 50 t =2 | 900 50 | t =2 18