The modelled equation for amount of radium after t years is,
[tex]R=30\cdot e^{-0.0031t}[/tex]
Substitute 10 for R in the equation and simplify the equation for t.
[tex]\begin{gathered} 10=30\cdot e^{-0.0031t} \\ e^{-0.0031t}=\frac{1}{3} \\ \ln (e^{-0.0031t})=\ln (\frac{1}{3}) \\ -0.0031t\ln (e)=-1.095612 \\ t=\frac{1.095612}{0.0031} \\ =354.391 \\ \approx354.4 \end{gathered}[/tex]
So after 354.4 years (approx), only 10 gram of radium is present.
