A thyroid cancer patient is given a dosage of 131I
(half-life = 8.1 d).
What fraction of the dosage of 131I will still be in the patient's thyroid after 32.4 days?
To find out what fraction of the dosage of 131I will still be in the patient's thyroid after 32.4 days, we can use the exponential decay formula:
N(t) = N0 * (1/2)^(t/T1/2)
Where:
N(t) = final amount of 131I in the patient's thyroid after time t
N0 = initial dosage of 131I given to the patient
t = time elapsed (32.4 days)
T1/2 = half-life of 131I (8.1 days)
Plugging in the values:
N(32.4) = N0 * (1/2)^(32.4/8.1)
N(32.4) = N0 * (1/2)^4
N(32.4) = N0 * (1/16)
After 32.4 days, only 1/16th of the initial dosage of 131I will still be in the patient's thyroid.