Answer
$R(t)=20+1.5 sin(1.16t)$
Work Step by Step
Step 1. Identify the quantities as $R_0=20,|a|=1.5,p=5.4$ where $R_0$ is the average radius, p=5.4 days is the period given in Example 4.
Step 2. Use a sine function to model the radius as $R(t)=R_0+|a| sin(\omega t)$ and with $p=\frac{2\pi}{\omega}=5.4$, we have $\omega=0.37\pi\approx1.16$. The function becomes $R(t)=20+1.5 sin(0.37\pi\ t)$ or
$R(t)=20+1.5 sin(1.16t)$
Step 3. Check the correctness of the function: as the average of a sine function is zero, the average of the radius is 20.
