Answer
$ t\approx 6.2$ hours.
Work Step by Step
Model: $ A=A_{0}e^{kt}$
Unknown: $ k $, when $ A=0.5A_{0},\ t=12$
$0.5A_{0}=A_{0}e^{k\cdot 12}\qquad... /\div A_{0}$
$0.5=e^{k\cdot 12}\qquad.../\ln(...)$
$-0.693147=12k\qquad.../\div(12)$
$ k\approx-0.057762$
So, our model is
$ A=A_{0}e^{-0.057762t}$
Now we find $ t $ for $ A=0.7A_{0}$
$0.7A_{0}=A_{0}e^{-0.057762t}\qquad... /\div A_{0}$
$0.7=e^{-0.057762t}\qquad.../\ln(...)$
$\ln 0.7 =-0.057762t\qquad.../\div(-0.057762)$
$\displaystyle \frac{\ln 0.7}{-0.057762}=t $
$ t\approx 6.2$ hours.
