Question

The San Francisco Bay tides vary between 1 foot and 7 feet. The tide is at its lowest point when time (t) is 0 and completes a full cycle in 8 hours. What is the amplitude, period, and midline of a function that would model this periodic phenomenon?

Amplitude = 6 feet; period = 8 hours; midline: y = 4
Amplitude = 6 feet; period = 4 hours; midline: y = 3
Amplitude = 3 feet; period = 8 hours; midline: y = 4
Amplitude = 3 feet; period = 4 hours; midline: y = 3

Answer 1

Amplitude = 3 feet; period = 8 hours; midline: y = 4

Explanation:

sketch it....(see attached)

Answer 2

The correct option is 3.

Explanation:

It is given that the San Francisco Bay tides vary between 1 foot and 7 feet.

It means the maximum value of the function is 7 and minimum value is 1.

The amplitude of the function is

`Amplitude=(Maximum-Minimum)/(2)`

`Amplitude=(7-1)/(2)=(6)/(2)=3`

The amplitude of the function is 3 feet.

Midline of the function is

`Midline=(Maximum+Minimum)/(2)`

`Midline=(7+1)/(2)=(8)/(2)=4`

The midline of the function is 4 feet.

It is given that the tide completes a full cycle in 8 hours. It means the period of function is 8 hours.

Therefore the correct option is 3.