Chapter 8.4, Problem 60PE

A patient undergoing a heart scan is given a sample of fluorine- $18\left({}^{18}\text{F}\right).$ After $4\text{ hr}$ , the radioactivity level in the patient is $44.1\text{ MBq}$ (megabecquerel). After $5\text{ hr,}$ the radioactivity level drops to $30.2\text{ MBq}\text{.}$ The radioactivity level $Q\left(t\right)$ can be approximated by $Q\left(t\right)=Q_0{e}^{-kt},$ where $t$ is the time in hours after the initial dose $Q_0$ is administered.

a. Determine the value of $k$ . Round to $4$ decimal places.

b. Determine the initial dose, $Q_0$ . Round to the nearest whole unit.

c. Determine the radioactivity level after $12\text{ hr}\text{.}$ Round to $1$ decimal place.