Answer to Question #170961 in Physics for gigi

Question

The half-life of a radioactive tracer injected into the human body is 7 days. If a patient is given a 30-mg dose of the tracer, then how many grams of tracer are still in the patient’s body after 21 days?

Answer 1

The mass of tracer are still in the patient’s body after $t = 21\space days$ is:

$$m = m_0 2^{-\frac{t}{T}}$$

where $m_0 = 30mg$ is the initial dose, $T = 7\space days$ is the half-life. Thus, obtain:

$$m = 30\cdot 2^{-\frac{21}{7}} = 3.75mg$$

Answer. 3.75 mg.