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Fluorodeoxyglucose is a derivative of glucose that contains the radionuclide fluorine-18 (18F). A patient is given a sample of this material containing 300 MBq of 18F (a megabecquerel is a unit of radioactivity). The patient then undergoes a PET scan (positron emission tomography) to detect areas of metabolic activity indicative of cancer. After 174 min, one-third of the original dose remains in the body.
a. Write a function of the form Q(t)=Q0e−kt to model the radioactivity level Q(t) of fluorine-18 at a time t minutes after the initial dose.
b. What is the half-life of 18F ? Round to the nearest minute.

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