Suppose that the fish population P(t) in a lake is attacked by a disease at time t = 0, wi...

Suppose that the fish population P(t) in a lake is attacked by a disease at time t = 0, with the result that the fish cease to reproduce (so that the birth rate is β = 0) and the death rate (deaths per week per fish) is thereafter proportional to 1/. If there were initially 900 fish in the lake and 441 were left after 6 weeks, how long did it take all the fish in the lake to die?