   Chapter 1.4, Problem 34E ### 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 alcohol is fully absorbed into the body, it is metabolized with a half-life of about 1.5 hours. Suppose you have had three alcoholic drinks and an hour later, at midnight, your blood alcohol concentration (BAC) is 0.6 mg/ mL.(a) Find an exponential decay model for your BAC t hours after midnight.(b) Graph your BAC and use the graph to determine when your BAC is 0.08 mg/mL.Source: Adapted from P. Wilkinson et al., “Pharmacokinetics of Ethanol after Oral Administration in the Fasting State,” Journal of Pharmacokinetics and Biopharmaceutics 5 (1977): 207–24.

(a)

To determine

To find: The exponential decay model for BAC t hours after midnight.

Explanation

Given:

The half-life of BAC is 1.5 hours.[BAC-Body Alcohol Concentration]

The level of BAC = 0.6mg/mL.

Calculation:

Let B0 be the initial level of BAC.[B-BAC]

That is B0=0.6mg/mL .

After 1.5 hours the level of BAC is B1=12B0

B1=12B0mg/mL

After 3 hours the BAC level as follows,

B2=12B1B2=12(12B0)B2=122B0mg/mL

After 4.5 hours the BAC level as follows,

B3=12B2B3=12(122B0)B3=123B0mg/mL

After 6 hours the BAC level as follows,

B4=12<

(b)

To determine

The time for BAC level is 0.08mg/mL.

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