Finding a Maximum from Rate Functions

The total number of people who have entered a museum is given by a function $f(t)$, and the total number of people who have left is given by a function $g(t)$, where $t$ is measured in hours since the museum opened. The respective rates are given by $f'(t) = 380(1.02^t)$ and $g'(t) = 240 + 240\sin\left(\frac{\pi(t - 4)}{12}\right)$. For the time interval $1 \leq t \leq 11$, at what time $t$ is the number of people in the museum at a maximum?