The concentration of alcohol $\displaystyle C$% in John's blood when he consumes alcohol could be represented by $\displaystyle C=0.3te^{-0.912t}$ where $\displaystyle t$ is the number of hours after he consumes alcohol.

Find the value of $\displaystyle t$ when the concentration of alcohol in John's blood is a maximum.

Attempt:

$\displaystyle 100=0.3te^{-0.912t}$

$\displaystyle \frac{100}{0.3}=te^{-0.912t}$

$\displaystyle \frac{100}{0.3}=lnt+lne^{-0.912t}$

$\displaystyle \frac{100}{0.3}=lnt-0.912t$

stucked