The given equation for the half life is
[tex] \frac{a}{2} =a e^{-3.392t} [/tex]
Divide each side by a to obtain
[tex] \frac{1}{2}= e^{-3.392t} [/tex]
Take the natural log of each side to obtain
ln(1/2) = -3.392t
Therefore
[tex]t= \frac{ln(1/2)}{-3.392} =0.2043[/tex]
Answer: t = 0.2043
