\begin{frame}
  \frametitle{Exponential Radioactive Decay}

  \begin{exampleblock}{}
    The half-life of radium-226 is $1590$ years.
    \begin{itemize}
    \pause
      \item We consider a sample of $100$mg.
    \end{itemize}
    \pause
    Find a formula for the mass that remains after $t$ years.
    \pause\medskip

    We have:
    \begin{talign}
      &m(t) = m(0) \cdot e^{-kt} \\
      &\mpause[1]{m(0) = 100} \\
      &\mpause[2]{m(1590) = \frac{1}{2}\cdot 100 = 50 \mpause[3]{= 100 \cdot e^{-k\cdot 1590}}} \\
      &\mpause[4]{e^{-k\cdot 1590} = \frac{1}{2} } 
      \mpause[5]{\;\;\implies\;\; -k\cdot 1590 = \ln \frac{1}{2} \mpause[6]{= \ln 1 - \ln 2 = -\ln 2} } \\
      &\mpause[7]{k = \frac{\ln 2}{1590} } 
    \end{talign}
    \pause\pause\pause\pause\pause\pause\pause\pause
    Hence $m(t) = 100e^{-\frac{\ln 2}{1590} t} \mpause[1]{= 100 \left(\frac{1}{2}\right)^{\frac{t}{1590}} }$ is the mass after $t$ years.\hspace*{-10ex}
  \end{exampleblock}  
\end{frame}