Chapter 3.6, Problem 26PE

Technetium-99 $\left({}^{99\text{m}}\text{Tc}\right)$ is a radionuclide used widely in nuclear medicine. ${}^{99\text{m}}\text{Tc}$ is combined with another substance that is readily absorbed by a targeted body organ. Then. special cameras sensitive to the gamma rays emitted by the technetium are used to record pictures of the organ. Suppose that a technician prepares a sample of ${}^{99\text{m}}\text{Tc}$ -pyrophosphate to image the heart of a patient suspected of having had a mild heart attack.

a. At noon, the patient is given 10 mCi (millicuries) of ${}^{99\text{m}}\text{Tc}$ . If the half-life of ${}^{99\text{m}}\text{Tc}$ is 6 hr, write a function of the form $Q\left(t\right)=Q_0{e}^{-kt}$ to model the radioactivity level $Q\left(t\right)$ after t hours.

b. At what time will the level of radioactivity reach 3 mCi? Round to the nearest tenth of an hour.