AP Calculus BC 5.11: Applied Minimum & Maximum Values

The number of people who have entered a museum on a certain day is modeled by a function f(t), where t is measured in hours since the museum opened that day. The number of people who have left the museum since it opened that same day is modeled by a function g(t). If $f^{\prime}(t)=380\left(1.02^{t}\right)$ and $g^{\prime}(t)=240+240 \sin \left(\frac{\pi(t-4)}{12}\right)$, at what time t, for $1 \leq t \leq 11$, is the number of people in the museum at a maximum?