Creating Your Own Real-World Scenario Involving Periodic Functions-What challenges did you face? Discuss what information you needed to include in order for the amplitude, midline, and period of your function to be computed.

Assignment Question

Creating Your Own Real-World Scenario Involving Periodic Functions

Part I: Complete the following steps: Select a real-world scenario that can be modeled by a periodic function (ex. temperature over time or tidal patterns). Write a mathematical expression for the function that can model your scenario. Find the amplitude, midline, and period of your function. Find the domain and range of your function. State the phase shift and vertical translation, if applicable. Part II: Based on your work in Part I, discuss the following: Discuss your rationale for your choice of real-world scenario. Reflect on your thought process as you created the scenario. What challenges did you face? Discuss what information you needed to include in order for the amplitude, midline, and period of your function to be computed. Discuss why the domain and range you found in Part I makes sense in this context. Discuss two possibilities for a change in the parameters of your scenario. How would your answers to Part I be affected by these changes? Provide at least two other real-world situations that can be modeled using a periodic function and respond to the following: What common characteristics do the real-world scenarios you chose share? What did you look for in the way that the real-world scenario can be modeled? How can you verify that the real-world scenarios you chose can be modeled by a periodic function? Discussion may include: Any real-world scenario involving periodic functions should show some time of pattern that repeats itself and should be able to be modeled using a periodic function. Students should reflect on the process in creating the scenario and discuss how it is modeled using a periodic function. All parameters must correspond to the function created by the student, and any change in parameter should affect the answers accordingly.