Question

The Chesapeake Bay tides vary between 4 feet and 6 feet. The tide is at its lowest point when time (t) is 0 and completes a full cycle in 12 hours. What is the amplitude, period, and midline of a function that would model this periodic phenomenon? Amplitude = 1 foot; period = 12 hours; midline: y = 5 Amplitude = 2 feet; period = 6 hours; midline: y = 1 Amplitude = 2 feet; period = 12 hours; midline: y = 5

Answer 1

Answer:

The correct option is 1.

Step-by-step explanation:

The general cosine function is

$y=A\cos (Bx+C)+D$

where, A is amplitude, $\frac{2\pi}{B}$ is period, C is phase shift and D is midline.

It is given that the Chesapeake Bay tides vary between 4 feet and 6 feet. it means the minimum value is 4 and maximum value is 6.

Amplitude of the function is

$Amplitude=\frac{Maximum-Minimum}{2}$

$Amplitude=\frac{6-4}{2}$

$Amplitude=1$

Therefore the amplitude of the function is y=5.

Midline of the function is

$Mid line=\frac{Maximum+Minimum}{2}$

$Mid line=\frac{6+4}{2}=5$

Therefore the midline of the function is y=5.

It completes a full cycle in 12 hours.

$Period=12$ hours

$\frac{2\pi}{B}=12$

Period of the function is 12 hours. Therefore the correct option is 1.

Answer 2

Answer:

A.  Amplitude = 1 foot; period = 12 hours; midline: y = 5