I. Goal

To use rational functions in a real-world situation

II. Role

You work in the research department of a prescription drug company.

III. Audience

The FDA (Food and Drug Administration)

IV. Situation

Your department has manufactured a new drug.

V. Task

Your department has manufactured a new drug, and you are required to make a presentation to the FDA regarding the concentration of the drug in a patient's bloodstream over time.

VI. Performance Task

Your department has found that the concentration of the new drug in a patient's bloodstream can be modeled by the equation

C(t) = 5t

t²+ 1

where C(t) represents the milligrams per liter of the drug and t represents the number of hours after the drug is administered.

You must prepare a presentation to be given to the FDA that includes the following:

• Identify the concentration of the drug in the patient's bloodstream after 1 hour, 2 hours, and 3 hours. Show all your calculations.
• Graph the asymptote, and identify and interpret the horizontal asymptote of the function.
• Make a convincing argument (1-2 paragraphs) for the continued production of this new drug.