Question

After an alcoholic beverage is consumed, 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 $$C(t)=0.135 t e^{-2302 t}$$ models the average BAC, measured in $\mathrm{g} / \mathrm{dL}$, 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 3 hours? When does it occur?

Name: Problem 73, Chapter 4: Calculus: Early Transcendentals
Uploaded: 2025-09-24T22:34:08-08:00
Duration: 1 min 51 s
Channel: James Kiss

   After an alcoholic beverage is consumed, 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 $$C(t)=0.135 t e^{-2302 t}$$ models the average BAC, measured in $\mathrm{g} / \mathrm{dL}$, 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 3 hours? When does it occur?

Calculus: Early Transcendentals

James Stewart,… 9th Edition

Chapter 4, Problem 73

Instant Answer

Solved by Expert James Kiss

09/24/2025

Step 1

135 t e^{-2.302 t}$ in the interval $0 \leq t \leq 3$. To find the maximum, we'll first find the critical points by taking the derivative and setting it equal to zero. Show more…

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After an alcoholic beverage is consumed, 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 $$C(t)=0.135 t e^{-2302 t}$$ models the average BAC, measured in $\mathrm{g} / \mathrm{dL}$, 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 3 hours? When does it occur?