3. Biomedical engineers are developing a new fertility drug. Absorption Elimination For it to be effective, enough drug must be present Pharmacokinetics in the blood for a sufficient period of time. The blood concentration of the drug (ug/ml) over time (h) determines the patient's overall drug exposure, which is the critical pharmacokinetic measure to determine dosing amounts. The critical overall exposure level for the new drug was determined to be 135 g-h/ml. Researchers gave the drug to an animal at time t=0, and monitored the drug blood concentration at regular intervals. The data are presented below: Blood Concentration of Drug (g/ml) Time Since Drug Delivery (h) 4 4 7 11 Amount of drug in blond Drig is taken 7 18 Cas Highest cancum of vid AUC (Area Under the Curve) D Time 3 2 25 32 39 a) Te 46 Cmini I drig b a. (4pts) Model the data as a 3rd degree polynomial and solve for the coefficients using the normal equations. b. (4pts) Using your model from (a), interpolate to find the expected blood concentration at 30 hours after taking the drug, and at 0 hours. In three sentences or less, are your results reasonable? c. (6pts) Use calculus to determine the time at which your model from part (a) predicts the animal will experience the maximum concentration of drug, Cmax, in its blood. What is the predicted value of Cmax? Give your answer in a complete sentence. d. (12pts) Use Lagrange Polynomials to construct a piecewise 3rd degree polynomial to model the data. Hint: Your polynomial will have two pieces. e. (6pts) Plot the data (as individual points), your interpolating polynomial from (a) as a smooth curve, your piecewise interpolating polynomial from (c) as a smooth curve, and the values of the interpolation found in part (b) as individual points, all on the same graph. Label your axes, and provide a legend. f. (8pts) Using the available data (not your models), estimate approximately how many hours after taking the drug you should wait before reaching the critical overall drug exposure level. Justify your answer in two sentences or less.