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 6 hours? (Round your answer to three decimal places.)

Accepted Solution

Answer:   about 0.177 mg/mLStep-by-step explanation:The maximum is found where the derivative of C(t) is zero.   dC/dt = 1.35e^(-2.802t) -(1.35t)2.802e^(-2.802t) = 0Solving for t gives ...   t = 1/2.802So, the maximum C(t) is ...   C(1/2.802) = 1.35/2.802e^(-1) ≈ 0.177 . . . . . mg/mLThe maximum average BAC during the first 6 hours is about 0.177 mg/mL._____The maximum occurs about 21 minutes 25 seconds after consumption.