## Calculus (3rd Edition)

The growth constant is $k=0.023$ and the plant population is $$P(t)=P_0e^{0.023 t}.$$ Also, $$1000=P_0e^{0.023 (48)}\Longrightarrow P_0=1000e^{-0.023 (48)}\approx 332 .$$
Since the doubling time is $30$, then we have $$\frac{\ln 2}{k}=30\Longrightarrow k= \frac{\ln 2}{30}=0.023.$$ So the growth constant is $k=0.023$ and the plant population is $$P(t)=P_0e^{0.023 t}.$$ Now, at $t=48$, we have $P=1000$: $$1000=P_0e^{0.023 (48)}\Longrightarrow P_0=1000e^{-0.023 (48)}\approx 332 .$$