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The Cobscook Bay tides vary between 4 feet and 20 feet. The tide is at its lowest point when time (t) is 0 and completes a full cycle in 18 hours. What is the amplitude, period, and midline of a function that would model this periodic phenomenon?
Amplitude = 16 feet; period = 9 hours; midline: y = 8
Amplitude = 16 feet; period = 18 hours; midline: y = 12
Amplitude = 8 feet; period = 9 hours; midline: y = 8
Amplitude = 8 feet; period = 18 hours; midline: y = 12

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luisejr77

Answer: Last Option

Amplitude = 8 feet; period = 18 hours; midline: y = 12

Step-by-step explanation:

This problem can be modeled by a sinusoidal function.

By definition the amplitude of a periodic function is half the distance between the minimum value and the maximum value of the function.

In this case we know that the minimum value is 4 and the maximum value is 20. Then the amplitude A is:

[tex]A = 0.5 (20-4)[/tex]

[tex]A = 8\ ft[/tex]

The middle line is a horizontal line that cuts the graph at its midpoint.

The midline is calculated as:

[tex]y = V_{max} - A[/tex]

Where A is the amplitude and Vmax is the maximum value of the function

[tex]y = 20-8[/tex]

[tex]y = 12[/tex]

Finally, the period is the time it takes for the function to complete a cycle. In this case we know that it takes 18 hours. So the period is 18 hours

The answer is: "Amplitude = 8 feet; period = 18 hours; midline: y = 12"

D.

Step-by-step explanation:

The above explanation is correct. I just took the exam, and my work is identical. Scored a 5/5 on the question. Don't know why it has bad reviews.

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