For this Critical Thinking assignment. you will be exploring a real-world example that can be modeled using a periodic function.
Begin by reading the following prompt:
A Ferris wheel is 25 meters in diameter and boarded from a platform that is 1 meter above the ground. The six o’clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 10 minutes. The function h(t) gives a person’s height in meters above the ground t minutes after the wheel begins to turn.
Part I: Complete the following steps:
1. Find the amplitude, midline, and period of h(t).
2. Find the domain and range of the function h(t) and
3. Find a formula for the height function h(t).
4. State the phase shift and vertical translation, if applicable.
5. How high off the ground is a person after 5 minutes?
6. Use the GeoGebra Graphing Calculator tool to model this situation. (Refer to this tutorial as needed: https://www.geogebra.org/m/XUv5mXTm n.) Save your GeoGebra work as a .pdf file for submission.
Part II: Based on your work in Part I. discuss the following:
1. In your own words, discuss why this situation can be modelled with a periodic function and how the information provided relates to the amplitude, midline. and period of the function h(t).
2. Discuss why the domain and range you found in Part I makes sense in the context of this problem.
3. Discuss how you found the height off the ground of the person after 5 minutes.
4. Discuss how your answers in Part I would be affected if:
a. The diameter of the Ferris wheel increased.
b. The time it takes for the Ferris wheel to complete 1 full revolution decreases.
5. Provide at least two other real-world situations that can be modeled using a periodic function and respond to the following:
a. What common characteristics do the real-world scenarios you chose share?
b. What did you look for in the way that the real-world scenario can be modeled?
c. How can you verify that the real-world scenarios you chose can be modeled by a periodic function?
