Answer
$B(t)=3.8+0.2 sin(\frac{\pi}{5}t)$
Work Step by Step
Step 1. Identify the quantities as $p=10, B_0=3.8, |a|=0.2$ where $B_0$ is the average brightness.
Step 2. Use a sine function to model the brightness as $B(t)=B_0+|a| sin(\omega t)$, and with $p=\frac{2\pi}{\omega}=10$, we get $\omega=\frac{\pi}{5}$ and the function becomes $B(t)=3.8+0.2 sin(\frac{\pi}{5}t)$
Step 3. Check the correctness of the function: as the average of the since function is zero, we have the average of
the brightness as B(average)=B_0=3.8
