If \( y \) is a positive quantity whose rate of change with respect to time is proportional to the quantity present at any time \( t \), then \( y \) is of the form \( y=C e^{k t} \), where \( C \) is the initial value and \( k \) the constant of proportionality.
To find an expression for half-life, put \( y=\frac{C}{2} \), half of the initial quantity, and \( t=h \), the half-life, in \( y=C e^{k t} \), then simplify.
\[
\begin{array}{l}
\frac{C}{2}=C e^{k h} \\
\frac{1}{2}=\square
\end{array}
\]