Fluorodeoxyglucose is a derivative of glucose that contains the radionuclide fluorine-18 18 F . A patient is given a sample of this material containing 300 MBq of 18 F (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 = Q 0 e − k t 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 18 F ? Round to the nearest minute.
Fluorodeoxyglucose is a derivative of glucose that contains the radionuclide fluorine-18 18 F . A patient is given a sample of this material containing 300 MBq of 18 F (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 = Q 0 e − k t 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 18 F ? Round to the nearest minute.
Solution Summary: The author analyzes the model for the quantity of radionuclide fluorine remaining in the patient's body at a time t minutes after being administered by using the exponential decay model.
Fluorodeoxyglucose is a derivative of glucose that contains the radionuclide fluorine-18
18
F
.
A patient is given a sample of this material containing 300 MBq of
18
F
(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
=
Q
0
e
−
k
t
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
18
F
? Round to the nearest minute.
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