Step 1:
Re-state the given function.
[tex]y=4\sin (\frac{\pi}{6}x)+9[/tex]Step 2:
We shall state the mathematical implication of the sine function at both minimum and maximum points.
At minimum point:
[tex]\begin{gathered} At\text{ minimum point: }\sin (\frac{\pi}{6}x)=-1 \\ \text{Similarly,} \\ At\text{ maxi}mum\text{ point: }\sin (\frac{\pi}{6}x)=1 \end{gathered}[/tex]Step 3: We shall substitute the values in step 2 above in the given function.
We are only interested in the value at maximum point, so
[tex]\begin{gathered} y=4(1)+9 \\ y=4+9 \\ y=13\text{ fe}et \end{gathered}[/tex]Thus, the correct answer is 13 feet ( option D)