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

True

$$t_d=\frac{1}{2}\ln (2)$$ The doubling time of a population governed by the Malthusian growth model is five minutes $$5=\frac{1}{k}\ln (2)\\ \rightarrow k=\frac{1}{5}\ln (2)$$ Substitute $P(t)=64$ and $k=\frac{1}{5}\ln (2)$ into Malthusian Model: $$P(t)=P_0e^{kt}\\ 64=e^{\frac{1}{5}\ln(2)t}\\ \frac{1}{5}\ln(2)t=\ln(64)\\ t=30$$ Hence, the initial population increases 64-fold in a half-hour.