1. While at a clinic in Carroll County, Maryland, a patient was given a dose of Xylopain, after which they lost consciousness. They were rushed to Carroll Hospital, where the level of the drug was checked hourly. The readings are recorded in the following table:

Hours elapsed since does of Xylopain

2 3 4 5 6 7 8

Concentration of Xylopain in mg/ml

6 4.25 3 2.12 1.5 1.06 0.75

(a) Find a function, C(t), that approximates the level of Xylopain in the patient's blood t hours after the drug was given to the patient. To test your function, C(t), show a graph of C(t) superimposed on a plot of the data points

(b) The patient, who recovered from the incident, has since discovered that the maximum allowable concentration of Xylopain is 10 milligrams per milliliter. They believe that the clinic exceeded this maximum recommended dosage and they plan to sue the clinic for negligence. Making use of the function you found in part (a), write a brief outline of the argument that the patient's attorney might make in court.

(c) In bullet points explain the incident, how data was collected, what analysis was done, why the patient is bringing the lawsuit and what conclusions the legal team is drawing from the analysis.