After the consumption of an alcoholic beverage, the concentration of alcohol in
ID: 2860366 • 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) = 1.35te?2.802t
†
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 to one alcoholic drink). What is the maximum average BAC during the first 4 hours? (Round your answer to three decimal places.)
22. 12 points SCalcET8 4.1.069 My Notes Ask Your Teacher 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 E(t) = 1.35te-2.802t t 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 to one alcoholic drink). What is the maximum average BAC during the first 4 hours? (Round your answer to three decimal places.) mg/mL When does it occur? (Round your answer to two decimal places.) Need Help? Read It Tlk to a Tutor Talk to a TutorExplanation / Answer
In order to find the max avg, take first derivative and set it to zero.
C(t) = 1.35te-2.802t
C'(t) = 1.35(e-2.802t - 2.802te-2.802t)
Equating to 0, we get 1.35(e-2.802t - 2.802te-2.802t) = 0, or 1.35e-2.802t (1- 2.802t) = 0
=> t = 1/2.802 hours = .357 hrs
Max BAC = 1.35te-2.802t , t = .357 = .177 mg/ml