We will have the following:
a)
[tex]\begin{gathered} A(10)=700^{-0.031(10)}\Rightarrow A(10)=513.4128694... \\ \\ \Rightarrow A(10)\approx513.41 \end{gathered}[/tex]
So, after 10 years the sample left will be approximately 513.42 g.
b) We determine the time it will take to get half the sample, that is:
[tex]\begin{gathered} 350=700e^{-0.031t}\Rightarrow\frac{1}{2}=e^{-0.031t}\Rightarrow ln(2)=-0.031t \\ \\ \Rightarrow t=\frac{ln(2)}{0.031}\Rightarrow t=22.35958647... \\ \\ \Rightarrow t\approx22.40 \end{gathered}[/tex]
So, it will take approximately 22.40 years.
