A state game commission releases 50 elk into a game refuge. After 5 years, the elk population is 110. The commission believes that the environment can support no more than 4200 elks. The growth rate of the elk population P is modeled by the logistic differential equation dP = kP(1- P/4200 ),  50 ≤ P ≤ 4200, where t is time in years. (a)Use the logistic equation P = L/(1+be^(-kt)) to write a model for the elk population in terms of time t by finding the values for b and k. (b) Use the model to estimate the elk population after 20 years.

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