Answer
$0.172$ mg/mL
Work Step by Step
Given: The function $C(t) =1.35te^{-2.802t}$
Calculate the maximum consumption of an alcoholic beverage, the concentration of alcohol in the bloodstream (blood alcohol concentration, or BAC) surges as the alcohol is absorbed, followed by a gradual decline as the alcohol is metabolized.
For this, we will have to take differentiae of the function
$C(t) =1.35te^{-2.802t}$
$C'(t)= 1.35(e^{-2.802t}-t(2.802)e^{-2.802t})$
Put $C'(t)=0$
$1.35(e^{-2.802t}-t(2.802)e^{-2.802t})=0$
$t=0.3569$ hours
Therefore, the maximum average BAC will be at $t=0.3569$ hours
This implies
$C(0.3569)=1.35(0.3569)e^{-2.802(0.3569)}=0.172$ mg/mL
