Answer
$y=3cos(\frac{\pi}{6}x)+9$
Work Step by Step
Step 1. Use the model function $y=AcosBx+D$ with the given information and graph.
Step 2. We can identify the average value as $y=9$ which means that $D=9$
Step 3. We can identify the amplitude as $y=\frac{12-6}{2}=3$ and thus $A=3$
Step 4. The period can be found as $p=18-6=12$, thus $\frac{2\pi}{B}=12$ and $B=\frac{\pi}{6}$
Step 5. The model function can be written as $y=3cos(\frac{\pi}{6}x)+9$
