A small ball floats on the surface of the water in a wave pool. As a wave moves past the ball, the ball's height above the bottom of the pool varies from 22 inches to 34 inches. The waves occur every
6 seconds. Which function models the distance from the bottom of the pool to the ball, as it moves
from wave crest to wave crest, as a function of t in seconds?
d(t) = 12 cos(3At) + 28
d (t) = 6 cos(3mt) + 28
34 in.
d(t) = 6 cos (+) +
+ 28
22 in
d(t) = 12 cos( 5 ) + 28

A function that models the distance from the bottom of the pool to the ball, as it moves  from wave crest to wave crest, as a function of t in seconds is

The standard wave equation is expressed as;

where:

A is the amplitude

Get the amplitude:

If the wave occurs every 3 seconds, then:

Get the midline D

Substitute the given parameters into the equation above to have;

Hence a function that models the distance from the bottom of the pool to the ball, as it moves  from wave crest to wave crest, as a function of t in seconds is

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The correct option is;

d(t) = 6·cos(π/3·t) + 28

Step-by-step explanation:

The general form of a cosine function is given as follows;

y = A·cos(B·x - C) + D

Where;

A = The amplitude = The distance from the peak to the midline = 1/2×(Maximum - minimum)

The amplitude = 1/2 × (34 - 22) = 6 inches

B = 2·π/P = 2·π/6 = π/3

P = The period = 6 seconds

C/B = The phase shift

D = The midline = Minimum  + Amplitude = 22 + 6 = 28 inches

x = The independent variable

Therefore, to model the function of the wave can be given as follows;

d(t) = 6·cos(π/3·t) + 28

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