After the consumption of an alcoholic beverage, the concentration of alcohol in
ID: 2851371 • Letter: A
Question
After the 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. The function
C(t) = 1.35te2.802t
†
models the average BAC, measured in mg/mL, of a group of eight male subjects t hours after rapid consumption of 15 mL of ethanol (corresponding toone alcoholic drink). What is the maximum average BAC during the first 3 hours? (Round your answer to three decimal places.)
when does it occur in hours ?
Explanation / Answer
C(t) = 1.35te2.802t
maximum when C '(t) = 0
==> 1.35(1)e2.802t + 1.35te2.802t(-2.802) = 0 since (uv)' = u'v + uv'
==> 1.35e2.802t - 3.7827te2.802t = 0
==> e2.802t(1.35 - 3.7827t) = 0
==> 1.35 - 3.7827t = 0 since e2.802t can never be equal to zero
==> t = 1.35/3.7827
==> t = 0.3568879
Hence after t = 0.357 hrs concentration is maximum