A Ferris wheel rotates around in 30 seconds. The maximum height above the ground is 55 feet, and the minimum height above the ground is 5 feet. Which function models the height as a function of t in seconds? (please write the full equation so i know which one it is, thank you!)

 Upper left corner

f(t) = 25sin( (pi/15)t ) + 30

Explanation:

One general way to write a trig function is to write

y = A*sin(B(x-C)) + D

where,

We are told that the highest point is at 55 ft off the ground, and the lowest point is 5 ft off the ground. The difference is 55-5 = 50 ft. This cuts in half to 50/2 = 25 ft. Therefore, the amplitude is |A| = 25 which will lead to A = 25. We'll just consider the positive A value to keep things simple.

Saying |A| = 25 means the vertical distance from the center to either the highest point, or lowest point, is 25 ft.

Then we're told that the wheel rotates every 30 seconds. This is the period of the function since the period is the length of time for a full cycle to happen, when the function repeats itself again.

Use T = 30 to find B

B = 2pi/T

B = 2pi/30

B = pi/15

With A = 25 and B = pi/15, we have enough info to see that the final answer is f(t) = 25sin( (pi/15)t ) + 30 which is in the upper left corner.

Note how D = 30 indicates the midline here. It tells us that we're 30 ft off the ground when we're at the halfway point between the highest and lowest markers of this wheel.

Notice further that D+A = 30+25 = 55 is the largest height value, and D-A = 30-25 = 5 is the smallest height value. This helps cement why this answer choice is correct. Try plugging in various values of t to find corresponding f(t) values. A table should help as well as making a graph. For every chunk of 30 seconds, the graph and table should repeat itself.