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} \\ \\ (\ln 0.5)/(-7.2)=-(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