I need an explanation for this Calculus question to help me study.
To complete this assignment, review the prompt and grading rubric in the Final Project Guidelines and Rubric document.
There are two possible scenarios for the final project in this course. You must choose only one of the following options, which are outlined in the Final Project Scenarios document: 1. Motion Problem 2. Decay Problem You will create a report that illustrates your final answer, process, explanations, and detailed solutions. You will defend the validity of your solutions and demonstrate your ability to effectively communicate using calculus notations, conventions, and terminology. The project includes one milestone, which is an important opportunity to submit a draft of Part II and ensure the accuracy of your calculations. This milestone will be submitted in Module Five. The final product will be submitted in Module Seven. In this assignment, you will demonstrate your mastery of the following course outcomes: Interpret real-world problems by selecting mathematical theorems that appropriately address the problem Utilize appropriate calculus techniques for solving real-world problems Determine the behavior of functions by analyzing a real-world model through appropriate calculus techniques Defend mathematical processes and solutions using appropriate calculus terminology Prompt Specifically, the following critical elements must be addressed: I. Introduction: In this section, you will briefly describe the mathematical theorem you selected, what you are trying to answer with your report, the approach for how you arrived at this selection, and the data points related to the rate of change of the object and how you will use them to arrive at your final results. 2 A. Briefly describe the mathematical theorems you selected and what you are trying to answer with your report. [MAT-223-01] B. Describe the approach for determining how you arrived at this selection. [MAT-223-01] C. Explain mathematically how the provided data will be used to arrive at your final results. [MAT-223-01] II. Analysis of Data: Applying Derivatives A. Using the given data, calculate the average acceleration of the changing object over given time intervals. [MAT-223-02] B. Using the given data, calculate the instantaneous acceleration at specific time values. [MAT-223-02] III. Analysis of Data: Applying Integrals A. Using the data provided, estimate the total change in the object. [MAT-223-02] 1. Use a right-endpoint estimate. 2. Use a left-endpoint estimate to approximate the total change of the object. 3. Calculate the best estimate for the total change of the object. B. Graph the model using the behavior of the functions represented by the data. [MAT-223-03] Note: To complete your graph, you can print graph paper at the Incompetech website, or you can complete a graph in Excel. The Microsoft Office website offers help with creating graphs in Excel. C. After completing your graph, discuss the relevance of the solution and how this graph represents it, using the calculus terminology of curve sketching. (Is the graph decreasing or increasing? How is this related to the data presented?) [MAT-223-04] IV. Analysis of the Model: Calculate Parts I and II. A. Given the model for each set of data, calculate the acceleration of the object using rules for differentiation. [MAT-223-03] B. Given the model for each set of data, calculate the total change of the object using rules for integration. [MAT-223-03] V. Final Results and Recommendations: In this section, you will conclude your report with your recommendations for a solution based on your findings. A. Compare the results obtained in Section II and Section III (Applying Derivatives and Applying Integrals) with the results in Section IV (Analysis of the Model). Discuss the accuracy of each method and explain the application of each method in a real-world context. [MAT-223-04] B. Defend your process of solving the problem by explaining a rationale for each process step. What does each step contribute to the ability to solve the problem and make recommendations? [MAT-223-04] C. Use calculus terminology to clearly explain your results and recommendations. Be sure to explain your answers using real-world terminology relevant to your topic in a way that is clear and understood.