Question

The tides around Cherokee Bay range between a low of one foot to a high of five feet. The tide is at its lowest point when time, t, is 0 and completes a full cycle over a 24 hour period. What is the amplitude, period, and midline of a function that would model this periodic phenomenon?
amplitude = 4 feet; period = 24 hours; midline: y = 3

amplitude = 2 feet; period = 12 hours; midline: y = 2

amplitude = 2 feet; period = 24 hours; midline: y = 3

amplitude = 4 feet; period = 24 hours; midline: y = 2

Answer 1

The answer is amplitude = 2 feet; period = 24 hours; midline: y = 3 

x1 - the lowest point
x2 - the highest point
x1 = 1 ft
x2 = 5 ft
t1 = 0
t2 = 24

The amplitude is: (x2 - x1)/2 = (5 - 1)/2 = 4/2 = 2 ft
The period is: t2 - t1 = 24 - 0 = 24 h
The midline is: (x1 + x2)/2 = (5 + 1)/2 = 6/2 = 3 ft