Question: Logistic Model. A population Pas a function of time t can be model by ODE. In a naturalgrowth case without limited resources, dP(d)t=kP for some

Logistic Model. A population Pas a function of time t can be model by ODE. In a naturalgrowth case without limited resources, dP(d)t=kP for some growth constant k. However,in reality an environment has limited resources and carries some carrying capacity M, themaximum population that itis capable of sustaining. The logistic differential equationincorporates these two ideas as follows:dP(d)t=kP(1-PM)Assume k and M are constants and P(0)=P0, solve the logistic ODE. You may refer 9.4 forthe details.

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