The logistic differential equation for population growth is dN = rN(1 - N/K) dt. The solution with initial condition N(0) = No is N(t) = No + (K - No)e^(-rt). Assume r, K, No > 0. For what populations N is the population increasing? decreasing? (ii) Explain why N = K is a stable equilibrium and interpret the constant K in terms of the model. (iii) By differentiating and using the Chain Rule, show that dN/dt = 2Nr(1 - N/K). (iv) Use this to show that there is a point of inflection when K = N and that this occurs at time t = (1/r)ln(No/(K - No)).