Answer
The growth constant is $ k=0.023 $ and the plant population is
$$ P(t)=P_0e^{0.023 t}.$$
Also, $$1000=P_0e^{0.023 (48)}\Longrightarrow P_0=1000e^{-0.023 (48)}\approx 332 .$$
Work Step by Step
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$:
$$1000=P_0e^{0.023 (48)}\Longrightarrow P_0=1000e^{-0.023 (48)}\approx 332 .$$
