Question

Over a 24-hour period, the tide in a harbor can be modeled by one period of a

Answer 1

The sinusoidal function that models the situation is:

$y = 4.5\sin{\left(\frac{\pi}{12}\right)x} + 5$

From the function, we have that:

• The amplitude is of 4.5 ft.

• The mid-line equation is of y = 5.

What is a sinusoidal function?

A sinusoidal function is a trigonometric function, and has the following format, considering no phase shift:

$y = A\sin{(Bx)} + C$

In which:

• A is the amplitude, which is the twice the difference between the largest and smallest value.

• The period is of $\frac{2\pi}{B}$.

• C is the vertical shift, and the mid-line equation is $y = C$.

In this problem, the high is of 9.5 ft and the low is of 0.5 ft, hence, for the amplitude, we have that:

$2A = 9$

$A = \frac{9}{2}$

$A = 4.5$

With an amplitude of 4.5, the standard function would vary between -4.5 ft and 4.5 ft, while in this problem the variation is from 0.5 ft to 9.5 ft, hence the vertical shift is of:

$C = 9.5 - 4.5 = 4.5 - (-0.5) = 5$

Which means that the mid-line equation is of y = 5.

Period of 24 hours, hence:

$\frac{2\pi}{B} = 24$

$24B = 2\pi$

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

Hence, the function is:

$y = 4.5\sin{\left(\frac{\pi}{12}\right)}x + 5$

You can learn more about sinusoidal functions at brainly.com/question/26384970