Question

PLEASE HELP!! 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?

A. Amplitude = 6 feet; period = 8 hours; midline: y = 4
B. Amplitude = 6 feet; period = 4 hours; midline: y = 3
C. Amplitude = 3 feet; period = 8 hours; midline: y = 4
D. Amplitude = 3 feet; period = 4 hours; midline: y = 3

Answer 1

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

Explanation:

If the Bay is 1 foot and 7 feet, and the tide is at its lowest at 0 and completes a full cycle every 8 hours. If every 8 hours is a new cycle the divide that by 2 to get the midline of 4 because for is the half way point for the full 8 hours

Hope this helped! :3

Answer 2

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

Explanation:

The midline is halfway between the lowest point and the highest point.

y = (1 + 7) / 2

y = 4

The period is the time it takes for a full cycle. So the period is 8 hours.

The amplitude is the distance from the midline to the lowest or highest point.

a = 4 − 1 = 3, or a = 7 − 4 = 3

It's also half the distance between the lowest and highest points.

a = (7 − 1) / 2

a = 3