Ferris Wheel Height

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?