A buoy starts at a height of 0 in relation to sea level and then goes up. Its maximum displacement in either direction is 6 feet, and the time it takes to go from its highest point to its lowest point is 4 seconds. Which of the following equations can be used to model h, the height in feet of the buoy in relation to sea level as a function of time, t, in seconds?

The equation of the model h will be h = 6 × sin(2πt/8). Then the correct option is C.What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.A buoy starts at a height of 0 in relation to sea level and then goes up. Its maximum displacement in either direction is 6 feet, and the time it takes to go from its highest point to its lowest point is 4 seconds.Then we have[tex]h=A \times \sin \omega t, \ \ at=0, \ \ h =0[/tex]The maximum displacement of the buoy in either direction is 6 ft, then we have[tex]h=6 \times \sin \omega t[/tex]The time it takes the buoy to get from the lowest to the highest point is 4 seconds then the oscillation time period will be 8 seconds. Then we have[tex]\omega T = 2\pi\\\\\omega = \dfrac{2\pi}{8}[/tex]Then the h will be given as[tex]h =6\times \sin (\dfrac{2\pi}{8}t)[/tex]More about the function link is given below.