Question: A limited growth model is useful when an ecosystem can only support up to a certain population size. If N is themaximum population size an

A limited growth model is useful when an ecosystem can only support up to a certain population size. If N is themaximum population size an ecosystem can support, then the rate of growth is proportional to the differencebetween the maximum population and the current population:dydt = k(N y )Suppose a salmon farm can hold up to a maximum of 50,000 fish.(a) Set up the differential equation that represents this situation.(b) Suppose that there are initially 2,000 salmon in the farm, and there are 25,000 salmon in the farm after3 months. Determine the solution to the differential equation.(c) Using your answer to part (b), how long would it take for the farm to reach 95% capacity? [Round youranswer to the nearest month.]

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