Prompt You have been hired by a company that has recently developed a medication designed to reduce the size of benign tumors. Your role is to confirm that the medication does reduce the size of the tumor, given the rate-of-change data. There are many factors to consider, and the goal is to determine the total change in the size of the tumor. Using this data, can you confirm that there is a change in the size ofthe tumor? Table | tin days 0 5 1O 15 20 25 30 35 40 45 r(t) in mm per day 0 -0.0105 -0.02093 -0.03134 -0.04171 -0.05204 -0.06234 {3.07261 -0.08283 -0.09303 Table II tin days 4 5 14 15 24 25 34 35 44 45 r(t) in mm per day -0.00839 -0.0105 0.02925 -0.03134 -0.04998 -0.05204 0.07056 0.07251 -0.09099 -0.09303 Part I: Introduction Describe the purpose and problem statement of this report. How did you use calculus to ensure that the medication is working to shrink the tumor? How is the rate of change data useful? Explain mathematically how the provided data was used to arrive at your final results. Part II: Analysis of Data Applying Derivatives A. Calculating average change in the rate of change. Using the data in Table I, calculate the average rate of change of the data for the following intervals: i. Fromt=0tot=45 ii. From t=25 tot=45 iii. From t=40 tot: 45 Southern New Hampsllfev University C. Discuss the relevance of these graphs, and how the rate of change graph is used to find the total change in the size of the tumor. Discuss the relationship between the two graphs using calculus terminology