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