Chapter 1 - First-Order Differential Equations - 1.5 Some Simple Population Models - True-False Review - Page 51: d

True

In logistic model, the population must be equal to carrying capacity $C$. Furthermore, the solution of logistic model can expressed as: $$P(t)=\frac{Cp_0}{P_0+(C-P_0)e^{-rt}}$$ If we take the limit of the model. $$limP(t)=C$$ we can see that it approaches the carrying capacity. Since the carrying capacity is constant and the derivative is the rate of change, the rate of change should be $0$. Hence, the statement is true.