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.)
1 answer:
Answer:
about 0.177 mg/mL
Step-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) = 0
Solving for t gives ...
t = 1/2.802
So, the maximum C(t) is ...
C(1/2.802) = 1.35/2.802e^(-1) ≈ 0.177 . . . . . mg/mL
The maximum average BAC during the first 6 hours is about 0.177 mg/mL.
_____
The maximum occurs about 21 minutes 25 seconds after consumption.
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