You have been hired by a company that has recently developed a medication designed to reduce...

 

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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 tin days r(t) in mm 0 5 10 15 20 0 -0.0105 -0.02093 -0.03134 -0.04171 25 -0.05204 30 -0.06234 35 -0.07261 40 -0.08283 45 -0.09303 per day Table II t in days 4 5 r(t) in mm -0.00839 -0.0105 14 -0.02926 15 -0.03134 24 -0.04998 25 -0.05204 34 -0.07056 35 -0.07261 44 -0.09099 45 -0.09303 per day A. Calculating average change in the rate of change. Using the data in Table I, calculate the average change in the rate of change data for the following intervals: From t=0 tot 45 i. ii. From t = 25 to t = 45 iii. From t = 40 tot = 45 B. Calculating instantaneous change in the rate of change. 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 rate of change. Use your results to explain why the limit definition of a derivative is true. 3. At what point is the rate of change at a maximum? How is this relevant to the size of the tumor? 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. 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 tin days r(t) in mm 0 5 10 15 20 0 -0.0105 -0.02093 -0.03134 -0.04171 25 -0.05204 30 -0.06234 35 -0.07261 40 -0.08283 45 -0.09303 per day Table II t in days 4 5 r(t) in mm -0.00839 -0.0105 14 -0.02926 15 -0.03134 24 -0.04998 25 -0.05204 34 -0.07056 35 -0.07261 44 -0.09099 45 -0.09303 per day A. Calculating average change in the rate of change. Using the data in Table I, calculate the average change in the rate of change data for the following intervals: From t=0 tot 45 i. ii. From t = 25 to t = 45 iii. From t = 40 tot = 45 B. Calculating instantaneous change in the rate of change. 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 rate of change. Use your results to explain why the limit definition of a derivative is true. 3. At what point is the rate of change at a maximum? How is this relevant to the size of the tumor? 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.