3. Modeling the Concentration of a Drug in the Bloodstream
A drug trial is studying the efficacy of a new drug for thalassemia, a genetic disorder in which a patient is unable to properly synthesize the hemoglobin molecule in the blood. In the trial, the rate at which the drug is metabolized by the body is studied. The data from the trial is then used to construct a model for the drugís metabolism. The concentration of a drug, in parts per million, in a patientís blood t hours after the drug is administered is given by the function
a) We would like to determine when the drug is completely eliminated from the bloodstream. Find this value of time, t. Explain why an exact solution to this problem is possible.
b) What is the mathematical domain of this function? What is the practical domain for this function?
c) Sketch the function on the mathematical domain and clearly show all your steps. As part of your graphing procedure, calculate some extra points to refine the accuracy of your graph. Clearly show which portion of your graph is in the practical domain of the problem. Explain the shape of the graph in the problem context and estimate when the drug attains maximum concentration.