Question

The depth of water at a dock can be modeled as y = 4 sin (62) + 9. At lowtide, the water is 5 feet deep. What is the depth of water at high tide (itsmaximum point)?A. 18 feetB. 14 feetC. 9 feetD. 13 feet

Answer 1

Step 1:

Re-state the given function.

$y=4\sin (\frac{\pi}{6}x)+9$

Step 2:

We shall state the mathematical implication of the sine function at both minimum and maximum points.

At minimum point:

$\begin{gathered} At\text{ minimum point: }\sin (\frac{\pi}{6}x)=-1 \\ \text{Similarly,} \\ At\text{ maxi}mum\text{ point: }\sin (\frac{\pi}{6}x)=1 \end{gathered}$

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

$\begin{gathered} y=4(1)+9 \\ y=4+9 \\ y=13\text{ fe}et \end{gathered}$

Thus, the correct answer is 13 feet ( option D)