Question

in the tidal area of a certain city, a sinusoidal function $f(x)=a\sin(b(x + c))+d$, where $a, b, c,$ and $d$ are constants, is used to model one cycle of high and low tides. the maximum value of the tide is 8.88 feet, and the minimum value of the tide is 0.54 feet in that cycle. if the values of $b, c,$ and $d$ have already been determined to fit the data, which of the following would best define $f(x)$?\
a $4.17\sin(b(x + c))+d$\
b $4.44\sin(b(x + c))+d$\
c $4.71\sin(b(x + c))+d$\
d $8.34\sin(b(x + c))+d$

Explanation:

Step1: Calculate amplitude $a$

The amplitude $a$ is half the difference between the maximum and minimum values of the sinusoidal function.
$a = \frac{\text{Max value} - \text{Min value}}{2} = \frac{8.88 - 0.54}{2}$

Step2: Compute the value of $a$

$a = \frac{8.34}{2} = 4.17$

Answer:

A. $4.17\sin(b(x + c)) + d$