Given the equation
[tex] \frac{a}{2} =ae^{-9.876t} \\ \\ \frac{1}{2} =e^{-9.876t} \\ \\ -9.876t=\ln\left( \frac{1}{2} \right)=-0.6931 \\ \\ t= \frac{-0.6931}{-9.876} =0.0702[/tex]
Therefore, the half life of the radioactive substance is 0.0702 days = 1.68 hours = 1 hour, 41 minutes, 4 seconds.
