Question

9. (09.03 MC)

The height of a certain Ferris wheel can vary from 2 feet to 102 feet off the ground. The Ferris wheel reaches its lowest height when time (t) is 0 and completes a full rotation in 40 seconds.
What is the amplitude, period, and midline of a function that would model this periodic phenomenon?
Amplitude 100 feet; period=40 seconds, midline: y = 52
Amplitude 100 feet period 20 seconds; midline: y = 50
Amplitude - 50 feet; period -20 seconds; midline: y = 52
Amplitude 50 feet; period 40 seconds; midline: y = 50

Answer 1

To determine the amplitude, period, and midline of a function that models the given Ferris wheel phenomenon, we need to analyze the information provided.

1. Amplitude: The amplitude represents half the distance between the maximum and minimum values of the function. In this case, the maximum height of the Ferris wheel is 102 feet, and the minimum height is 2 feet. Therefore, the amplitude is (102 - 2) / 2 = 100 feet.

2. Period: The period represents the time it takes for the function to complete one full cycle. In this case, the Ferris wheel completes a full rotation in 40 seconds. Thus, the period is 40 seconds.

3. Midline: The midline represents the horizontal line that serves as the average or midpoint of the function. In this case, the Ferris wheel's lowest height occurs at t = 0, and it varies from 2 feet to 102 feet. Thus, the midline is the average of these two extremes, which is (2 + 102) / 2 = 52 feet.

Based on this analysis, the correct answer is:
Amplitude: 100 feet
Period: 40 seconds
Midline: y = 52