Chapter 3.5, Problem 71PE

Physicians often treat thyroid cancer with a radioactive form of iodine called iodiro-131 $\left({}^{131}\text{I}\right)$ . The radiological half-life of ${}^{131}\text{I}$ is approximately 18 days, but the biological half-life for most individual is 4.2 days. The biological half-Ida is shorter because in addition to ${}^{131}\text{I}$ being lost to decay, the iodine is also excreted from the body in urine, sweat, and saliva. For a patient treated with 100 mCi (millicuries) of ${}^{131}\text{I}$ , the radioactivity level R (in mCi) after t days is given by $R=100{\left(2\right)}^{-t/4.2}.$

a. State law mandates that the patient stay in an isolated hospital room for 2 days after treatment with ${}^{131}\text{I}$ . Determine the radioactivity level at the end of 2 days. Round to the nearest whole unit.

b. After the patient is released from the hospital, the patient is directed to avoid direct human contact until the radioactivity level drops below 30 mCi. For how many days after leaving the hospital will the patient need to stay in isolation? Round to the nearest tenth of a day.