Question

At midnight the water at a particular beach is at high tide. At the same time a gauge at the end of a pier reads 10 feet. Low tide is reached at 6 AM when the gauge reads 4ft.

Answer the questions that follow using this scenario.


Sketch the graph of this situation assuming the cycle repeats. Show at least 2 cycles. Label the x- and y-axes with the appropriate scale and title. Upload your sketch.

Answer 1

Refer to the figure shown below.

From midnight (high tide) to 6 AM (low tide) is 6 hours, and it is half the period.
Therefore the period is
T = 12 hours.

Half the difference between 10 ft and 6 ft is the amplitude.
The amplitude is
A = 3 ft

On a graph of x versus t, where x = height (ft) after t hours, the mathematical model is

`x(t)=3cos( ( \pi t)/(6))+7 \,ft \\ where\\ t=time,\, hours`

The graph of the mathematical model agrees with the illustrated sketch, as shown.