Modelling Drug Concentration

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 drug's metabolism. The concentration of a drug, () in parts per million, in a patient's blood hours after the drug is administered is given by the function

() = 5 +34 63 22 +60

The goal of this tutorial is to graph this function and analyze and interpret the graph within the problem context.

Show the following steps on the blackboard or paper as your instructor directs:

a) State the coordinates of the y-intercept. Explain the meaning of this intercept within the problem context.

b) Use the procedure in Unit 2 Chapter 5 (p.211) to solve for all the zeros of f(t). Show clearly all steps of this procedure, identify the fully factored form of f(t) as part of the process.

c) Which of the zeros found in part b) are t-intercepts? Explain the meaning of the intercepts within the problem context.

d) Use the procedure for sketching polynomial functions (p. 189) to sketch the graph for f(t). Show clearly all steps of this procedure.

e) Identify the practical domain on your graph and state the practical domain in interval notation.

f) Using your graph, estimate when the drug attains maximum concentration. Check your answer by using graphing software (graphing calculator, wolframalpha phone app or website, desmos.com, etc).