Question: Problem 6: As a final model, let us assume that Gompertz equation can be used to describe the population of fish. As before we

Problem 6: As a final model, let us assume that Gompertz equation can be used to describe the population of fish. As before we assume a birth rate of a 5 and the same initial condition, so that we have to solve the IVP = (a) Solve this IVP. dP dt = - P(5 In P), P(0) = 1. (b) Plot and attach the solution for 0 t 3 and a suitable P-range. (c) In fact, Gompertz equation is NOT a good model for a fish population (instead it has been used to model tumor growth), as compared to the well established logistic equation used in Problems 3 and 4. Can you explain this by looking at the large time behavior of the solution you find in part (a)?

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