A fish hatchery has 500 fish at time t = 0, when harvesting begins at a rate of b fish/yr, where b > 0. The fish population is modeled by the initial value problem

y'(t) = 0.1y - b, y(0) = 500 for t ≥ 0,

where t is measured in years.

a. Find the fish population for t ≥ 0 in terms of the harvesting rate b.

b. Graph the solution in the case that b = 40 fish/yr. Describe the solution.

c. Graph the solution in the case that b = 60 fish/yr. Describe the solution.