Question

On Orca Beach, the high tide is 2 meters and only occurs at 12 a.m. and 12 p.m. The low tide is 0.8 meter and only occurs at 6 a.m. and 6 p.m. Which function models the height of the tide t hours after 12 a.m.?

Choices:

1. h(t)=2cos(πt/3)+0.8

2. h(t)=0.6cos (πt/6) + 1.4

3. 0.6sin(πt/6) + 1.4

4. 1.4sin (πt/3) + 2

Answer 1

2. h(t)=0.6cos (πt/6) + 1.4

Explanation:

The average water level is (2 +0.8)/2 = 1.4, so this is the offset that is added to the sine or cosine function. That eliminates choices 1 and 4.

The high tide occurs when t=0 (at 12 AM), so eliminating choice 3.

The function that models the height of the tide t hours after 12 AM is ...

h(t)=0.6cos (πt/6) + 1.4