Question

I do not understand how to work this type of problem. The logistic growth model is dP/dt = kP(1-P/M) or dP/dt = (k/M)P(M-P) where P is population, k is aconstant growth rate and M is the carrying capacity. The question I'm having trouble with is dP/dt = 0.04P - 0.0004P^2 and I am supposed to find k and M, I have noidea where to even start

Answer 1

Distributing the logistic growth model gets dP/dt = kP-kP^2/M with each term equal to the corresponding term in your question dP/dt = 0.04P - 0.0004P^2. You can easily see that k=0.04. To find M, set the second terms equal and cancel out the P^2 to solve. 0.0004P^2=kP^2/M. Use the previously obtained value of k and work it out.