   Chapter 4.1, Problem 69E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# 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 ) = 1.35 t e − 2802 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 3 hours? When does it occur?

To determine

To find: The maximum average BAC (blood alcohol concentration) during the first 3 hours.

Explanation

Given:

The function of BAC is given by C(t)=1.35te2.802t

Calculation:

The function is C(t)=1.35te2.802t .

For the convenience consider m=1.35 and n=2.802 . Then the above equation becomes C(t)=mtent .

Then consider, t=elnt . Then the function becomes,

C(t)=melntent=me(lntnt)

Let x=lntnt .

Obtain the derivative of x.

x=ddt(lntnt)=1tn

Set x=0 to find the maximum value

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