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

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:

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

The midline is calculated as:

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

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"