1. Using the data in Table II, calculate the instantaneous acceleration at the following intervals: i. t = 5 ii. t = 15 iii. t = 25 iv. t = 35 v. t = 45 2. Explain how you used the limit definition of a derivative to calculate the instantaneous acceleration. Use your results to explain why the limit definition of a derivative is true. 3. At what point is the acceleration at a maximum? How is this relevant to the landing aircraft? For each of the questions above, provide supporting solutions and calculus terminology to explain how you arrived at your answers. Also, explain in detail what your answer represents in a real-world context and why this is useful. Scenario Two: Decay Problem 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 of the tumor? Table I t in days 0 5 10 15 20 25 30 35 40 45 rit) in mm 0 -0.0105 -0.02093 0.03134 -0.04171 -0.05204 -0.06234 -0.07261 0.08283 0.09303 per day Table II t in days 4 5 14 15 24 25 34 35 44 45 rit) in mm -0.00839 -0.0105 -0.02926 -0.03134 -0.04998 -0.05204 -0.07056 -0.07261 -0.09099 -0.09303 per day