A is the initial population
b is the decay coefficient
X is normally the time.
[tex]Y = Ae^{-bx}[/tex]
then is the population half of the initial population of A
for half life you will have
[tex]\frac{Y}{A} = \frac{1}{2}[/tex]
so the equation becomes
[tex]\frac{1}{2} = e^{-bX}
\\
\\\ln{ \frac{1}{2}} =\ln{e^{-bX}}
\\
\\ \ln{1}-\ln{2}=-bX
\\bX=\ln{2}[/tex]
