3. (40pts) You are developing a new drug to treat cardiovascular calcification. The drug is administered as a pill and is absorbed into the blood stream over time. It is imperative to ensure the blood concentration of the drug never exceeds the limit of 120 micrograms*t/ml. This limit is based on the overall drug exposure which is the area under the curve of the plot of concentration of the drug over time. In order to ensure this limit is not exceeded you collect the following data from the patient over a 50-hour time. Drug Concentration in 68 8 4 4 3 1 Blood Time (Hours) 310 14 18 25 32 50 a. Model the data as a 30 degree polynomial and solve for the optimal coefficients b. Using your model from a.) interpolate the data to find the expected drug concentration at 30 hours and 0 hours. In 3 sentences or less are your results reasonable and why. c. Using Calculus determine the time at which your model predicts maximum drug concentration. What is the predicted maximum drug concentration? d. Using Lagrange polynomials construct 3" degree polynomials to interpolate the data by hand. e. Plot the data (as individual points), your interpolating polynomial from (a) as a smooth curve, your piecewise interpolating polynomials from (c) as smooth curves, 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. Using trapezoidal method compute the area under the curve of the data (not your models) and determine how many hours it takes to reach the limit of 120 micrograms*t/ml (i.e at what time does the area to reach this number?)