Question

The Saginaw Bay tides vary between two feet and eight feet. The tide is at its lowest point when time (t) is 0 and completes a full cycle in 16 hours. What is the amplitude, period, and midline of a function that would model this periodic phenomenon?

Answer 1

Answer:  Amplitude = 3, period = 16 hours and midline is y=5.

Step-by-step explanation: Given that the Saginaw Bay tides has minimum point at 2 feet and maximum point is at 8 feet.

To find the amplitude, period and midline of the function that would model this periodic phenomenon.

See the attached graph of the periodic function. The minimum point is A(4.5,2) and the maximum point is B(1.5,8).

The midline of the function is

$y=\dfrac{2+8}{2}\\\\\Rightarrow y=5.$

The amplitude is the perpendicular $A=8-5=5-2=3.$distance between the midline and one of its extreme point. So, amplitude is given by

$A=8-5=5-2=3.$

Also, period is the time taken by the waves to travel from one maximum point to another i.e., between two consecutive maximum points or minimum points.

So, period of the function is 16 hours.

Thus, amplitude = 3, midline is y=5 and period of the function is 16 hours.

Answer 2

The problem ask to compute the amplitude, period and the midline of the function represented in the problem. In my calculation, the period would be 16 hours, the amplitude is 3 feet and the mid line is 5. I hope you are satisfied with my answer and feel free to ask for more.