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

True

The concavity can be expressed as: $$\frac{d^2 P}{dt^2}[f(t)]$$ Take the derivative of the logistic model $$\frac{d}{dt}\frac{dP}{dt}=kP$$ At some point the derivative is 0: $\frac{d^2 P}{dt^2}=0$ Hence, the concavity does not depend on $k$ so for the Malthusian growth model the concavity doesn't change.