The fish population in a pond with carrying capacity 2000 is modeled by the following logistic equation where M!) denotes the number of sh at time tin years. dN 0.4 = N 2000 N dt 2000 l ) Starting at the time at which the number of sh reached 250, the owner of the pond removed (harvested) fish at a constant rate of 75 fish per year. We take it = 0 to be the time at which the owner started to harvest fish from the pond. (a) Modify the differential equation to model the population of sh from the time it reached 250. dN_ 0.4 7 7 F_ TUOOngUUU N) 75 \\I (b) Sketch several solutions of the new equation, including the solution curve with N(0) = 250. (This will not be graded.) (c) [s the practice of catching 75 fish per year sustainable or will it totally deplete the fish population in the pond? (You will have only one submission for this answer. Use your submission wisely!) (9 Yes, it is sustainable. No, it is unsustainable. ~/ (d) How far below the original carrying capacity will the number of fish be in the long run? (Give your answer correct to the nearest whole fish.) 1000 x fish