Chapter 9.4, Problem 5E

The Pacific halibut fishery has been modeled by the differential equation

$\frac{dy}{dt}=ky\left(1-\frac{y}{M}\right)$

where y(t) is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be M = 8 × 10⁷ kg, and k = 0.71 per year.

(a) If y(0) = 2 × 10⁷ kg, find the biomass a year later.

(b) How long will it take for the biomass to reach 4 × 10⁷ kg?