Answer
$P(t)=100e^{\frac{\ln 2}{7}t}$
Work Step by Step
Find $k$ and $C$.
The doubling time is:
$$t_{\frac{1}{2}}=\frac{\ln 2}{k}$$
$$7=\frac{\ln 2}{k}$$
$$k=\frac{\ln 2}{7}$$
so:
$$P(t)=Ce^{\frac{\ln 2}{7}t}$$
Since $P(0)=100$ it follows that $100=Ce^{\frac{\ln 2}{7}\cdot 0}=C$
Therefore, the equation is:
$$P(t)=100e^{\frac{\ln 2}{7}t}$$
