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18 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 minutes, 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. Round the value of k to five decimal places. Do not round intermediate calculations.
(b) What is the half-life of ¹⁸F? Round to the nearest minute. Do not round intermediate calculations.
Sagot :
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