A modification of the logistic model is given by the model of Schaefer dP/dt = 1/τ (1-P/K)P- EP. The model, which was developed for the simulation of the development of fish populations, is equivalent to the logistic model for E = 0, where L P(-[infinity]) = 0) is assumed for simplicity. The last term -E P takes into account (human) predation that reduces the rate of population growth. It is reasonable to consider this term to be proportional to P: the effect of predation will increase with the population density. The variables K, E< 1/ τ, and τ are assumed to be non-negative and constant. a) Write the model in the form of the logistic model (the structure of this rewritten model will be equal to the logistic model but the parameters are different). b) Calculate the solution of this rewritten model by taking reference to the solution of the logistic model. c) Explain the effect of a nonzero E on the population dynamics in comparison to the logistic model.