Answer
$y=cos(\frac{\pi}{6}x)+4$
Work Step by Step
Step 1. Use the model function $y=AcosBx+D$ with the given information and graph.
Step 2. We can find the average value as $y=\frac{5+3}{2}=4$, which means that $D=4$
Step 3. We can identify the amplitude as $y=\frac{5-3}{2}=1$ and thus $A=1$
Step 4. The period can be found as $p=12-0=12$, thus $\frac{2\pi}{B}=12$ and $B=\frac{\pi}{6}$
Step 5. The model function can be written as $y=cos(\frac{\pi}{6}x)+4$
