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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.