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

Answer:

The correct option is 3.

Step-by-step 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

$Amplitude=\frac{Maximum-Minimum}{2}$

$Amplitude=\frac{7-1}{2}=\frac{6}{2}=3$

The amplitude of the function is 3 feet.

Midline of the function is

$Midline=\frac{Maximum+Minimum}{2}$

$Midline=\frac{7+1}{2}=\frac{8}{2}=4$

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.

Answer 2

Answer:

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

Step-by-step explanation:

sketch it....(see attached)