Question

The half life of iodine-131 is 7.2 days. If you start with 80 milligrams of iodine-131, how much of the substance will remain after 36 days?

Answer 1

Given

The half-life of iodine-131 is 7.2 days. If you start with 80 milligrams of iodine-131, how much of the substance will remain after 36 days?

Solution

$\begin{gathered} 0.5=e^{-7.2k} \\ \ln 0.5=-7.2k \\ \text{divide both sides by -7.2} \\ \\ \frac{\ln 0.5}{-7.2}=-\frac{7.2k}{-7.2} \\ \\ k=0.09627044174 \\ \end{gathered}$$\begin{gathered} A=80e^{-kt} \\ A=80e^{-0.09627044174(36)} \\ A=2.5\text{miligrams} \end{gathered}$

2.5 milligrams will remain after 36 days