7. a local fishing site contains an estimated 50,000 fish, with a natural population growth rate of 5% per year. the annual catch by local fisherman depletes this population by about 3,000 fish per year. a) set up a differential equation that models the growth of the fish population, taking into account the effect of fishing. state as clearly the fish population this model is based on. as you can what physical assumptions about b) using qualitative analysis sketch a graph of the population vs. time. explain briefly how this graph is obtained. c) based on your answer in b) can the current annual catch be sustained indefinitely? confirm the result by finding the exact solution of the equation in a). (in regard to solving the equation, see the note to