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 ((\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 ((\pi)/(6)x)=-1 \\ \text{Similarly,} \\ At\text{ maxi}mum\text{ point: }\sin ((\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)