​ What is the equation for the sine function f(x), where x represents time in hours since the beginning of the 24-hour period, that models

This one is a little difficult......

Here's the form of the function that we need :

f(x)  = Asin (Bx)  + C

The amplitude, A, can be determined by  taking the [high point - the midline point ]  =

8.3  - 4.35  =  3.95

"C"   will be the midline point  = 4.3

B"  is the harder to determine.....we want to divide 2pi by 24  = pi / 12  = B

So  our function is

f(x)  =  3.95sin [ pi/12 * x ]  + 4.35

Here's the graph :

https://www.desmos.com/calculator/1ox0tmscf7

Note that  at  =  0 [ midnight ] we are at 4.35 ft

At x = 6  [ 6AM]  we are at high tide = 8.3 ft

At   x = 12  [noon] we are back to 4.35 ft

At x  = 18  [ 6PM] we are at low tide  = 0.4 ft

At x  = 24  [ midnight, again ] we are back to the midline