Option #2:** Creating Your Own Real-World Scenario Involving Periodic Functions**

For this Critical Thinking assignment, you will create your own real-world scenario that can be modeled using a periodic function.

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.

Requirements:

You must submit two files for this assignment. The first file should contain the computations, graphs, diagrams, etc., associated with the questions in Part I. This file may be formatted as a numbered list of answers. Unless stated in the problem, a narrative discussion is not required, but you must provide enough information to show how you arrived at the answer.

The second file should be a 2-3 page narrative paper, written in APA format, associated with the situation described in Part II. Specific requirements for the paper are provided below:

- Your paper should be 2-3 pages in length (not counting the title page and references page) and cite and integrate at least two credible outside sources.
- Include a title page, introduction, body, conclusion, and a reference page.
- The introduction should describe or summarize the topic or problem. It might discuss the general applications of the topic or it might introduce the unique terminology associated with the topic.
- The body of your paper should address the questions posed in the problem. Explain how you approached and answered the question or solved the problem, and, for each question, show all steps involved. Be sure this is in paragraph format, not numbered answers like a homework assignment.
- The conclusion should summarize your thoughts about what you have determined from your analysis in completing the assignment. Nothing new should be introduced in the conclusion that was not previously discussed in the body paragraphs.

- Include any tables of data or calculations, calculated values, and/or graphs referenced in the paper. (Note: The minimum required length excludes any tables, graphs, etc.)