2. a biologist studies a population of fish in a lake, and observes that the number n(t) (measured in thousands of fish in the lake at time t years is governed by the differential equation dn/dt = n - 1/2n^2 currently there are 800 fish in the lake (that is, n(0) = 0.8). (a) give a brief physical interpretation of each term on the right hand side of the differential equation. (b) suppose now that fish are harvested from the lake at a constant rate of h thousand fish per year. construct a differential equation incorporating this new information into the above model, and determine the value of h that keeps the fish population constant at 800 fish. (c) it is decided that fish will be harvested from the lake at a constant rate of 500 fish per year. solve your differential equation from the previous part with h = 0.5. (d) is the harvesting rate of 500 fish per year sustainable? justify your answer. (e) after 6 years of harvesting fish at a rate of 500 fish per year, there is a complete ban placed on fishing in the lake. how long will it take for the population to return to 800 fish?