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

True

The Malthusian growth doubling time is: $t_d=\frac{\ln 2}{k}$ Substitute for $k$: $10=\frac{\ln 2}{k}\\ \rightarrow k=\frac{1}{k}\ln(2)$ For the population to increase 10 fold: $10P_0=P_0e^{kt}\\ 10P_0=P_0e^{\frac{1}{10}\ln(2)t}\\ \rightarrow \ln (10)=\frac{1}{10}\ln(2)t\\ \rightarrow 10\frac{\ln(10)}{\ln(2)}=t\\ \rightarrow t\approx 33$ Hence, the statement is true.