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. 6 8 8 4 4 3 1 Drug Concentration in Blood Time (Hours) 3 10 14 18 25 32 50 a. Model the data as a 3rd 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 3rd degree polynomials to interpolate the data by hand