4. harvesting a renewable resource suppose that the population p of a certain species of fish in a given area of the ocean is described by the logistic equation if the population is subjected to harvesting at a rate h(p, t) members per month, then the harvested population is modeled by the differential equation de = k (1- p-h(p, t). (2) although it is desirable to utilize the fish as a food source, it is intuitively clear that if too many fish are caught, then the fish population may be reduced below a useful level and possibly even driven to extinction. the following problems explore some of the questions involved in formulating a rational strategy for managing the fishery! constant effort harvesting at a given level of effort, it is reasonable to assume that the rate at which fish are caught depends on the population p: the more fish there are, the easier it is to catch them. thus we assume that the rate at which fish are caught is given by hp, t) = ep, where is a positive constant, with units of '1/month', that measures the total effort made to harvest the given species of fish. with this choice for h(p, t), equation (2) becomes de = (1- p- ep (3) (this equation is known as the schaefer model after the biologist m. b. schaefer.) (a) (1 point) show that there are two equilibrium points, pi = 0 and p2 = n(1 – e/k). (b) (1 point) assume e 0. also, classify the equilibrium points (source, sink, or node) only for p2. (c) (1 point) sketch several graphs of solutions.