Chapter 1.4, Problem 34E

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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

That is

After 1.5 hours the level of BAC is

After 3 hours the BAC level as follows,

After 4.5 hours the BAC level as follows,

After 6 hours the BAC level as follows,

(b)

To determine

The time for BAC level is 0.08mg/mL.

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