The Chesapeake Bay tides vary between 4 feet and 6 feet. The tide is at its lowest point when time (t) is 0 and completes a full cycle in 12 hours. What is the amplitude, period, and midline of a function that would model this periodic phenomenon?

Amplitude = 1 foot; period = 12 hours; midline: y = 5

Amplitude = 2 feet; period = 6 hours; midline: y = 1

Amplitude = 2 feet; period = 12 hours; midline: y = 5

Respuesta :

Answer:

Amplitude = 1 foot; period = 12 hours; midline: y = 5

Step-by-step explanation:

The Chesapeake Bay tides vary between 4 feet and 6 feet.

This means the range is

[tex]4 \leqslant f(t) \leqslant 6[/tex]

The period is the length of the interval on which the function completes one full cycle.The tide is at its lowest point when time (t) is 0 and completes a full cycle in 12 hours.

The interval is [0,12] and its length is 12, hence the period is 12.

The midline

[tex]y = \frac{min + max}{2} [/tex]

[tex]y = \frac{4 + 6}{2} = 5[/tex]

The amplitude is the distance from the midline to the peak.

The amplitude is |5-4|=|5-6|=1

The first choice is correct.