Question

How many years will only 10 G of radium be present

Answer 1

The modelled equation for amount of radium after t years is,

`R=30\cdot e^(-0.0031t)`

Substitute 10 for R in the equation and simplify the equation for t.

`\begin{gathered} 10=30\cdot e^(-0.0031t) \\ e^(-0.0031t)=(1)/(3) \\ \ln (e^(-0.0031t))=\ln ((1)/(3)) \\ -0.0031t\ln (e)=-1.095612 \\ t=(1.095612)/(0.0031) \\ =354.391 \\ \approx354.4 \end{gathered}`

So after 354.4 years (approx), only 10 gram of radium is present.