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

2. h (t) = 0.6cos (πt/6) + 1.4

Step-by-step 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