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Calculus / Calculus with Applications 10 / Chapter 2.3 / Problem 55A

Calculus with Applications | 10th Edition | ISBN: 9780321749000 | Authors: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

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Alcohol Concentration The polynomial functionA(x) =

Chapter 2, Problem 55A

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QUESTION:

Problem 55A

Alcohol Concentration The polynomial function

A(x) = 0.003631x3 − 0.03746x2 + 0.1012x + 0.009

gives the approximate blood alcohol concentration in a 170-lb woman x hours after drinking 2 oz of alcohol on an empty stomach, for x in the interval [0, 5]. Source: Medical Aspects of Alcohol Determination in Biological Specimens.

a. Graph A(x) on 0 ≤x ≤ 5.

b. Using the graph from part a, estimate the time of maximum alcohol concentration.

c. In many states, a person is legally drunk if the blood alcohol concentration exceeds 0.08%. Use the graph from part a to estimate the period in which this 170-lb woman is legally drunk.

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QUESTION:

Problem 55A

Alcohol Concentration The polynomial function

A(x) = 0.003631x3 − 0.03746x2 + 0.1012x + 0.009

gives the approximate blood alcohol concentration in a 170-lb woman x hours after drinking 2 oz of alcohol on an empty stomach, for x in the interval [0, 5]. Source: Medical Aspects of Alcohol Determination in Biological Specimens.

a. Graph A(x) on 0 ≤x ≤ 5.

b. Using the graph from part a, estimate the time of maximum alcohol concentration.

c. In many states, a person is legally drunk if the blood alcohol concentration exceeds 0.08%. Use the graph from part a to estimate the period in which this 170-lb woman is legally drunk.

ANSWER:

SOLUTION:

Step 1 of 4:

In this question, the polynomial function gives the approximate blood alcohol concentration in a 170-lb woman hours after drinking 2 oz of alcohol on an empty stomach, for in the interval [0, 5]. (a) Graph on . (b) Using the graph from part (a), estimate the time of maximum alcohol concentration. (c) In many states, a person is legally drunk if the blood alcohol concentration exceeds 0.08%. Use the graph from part a to estimate the period in which this 170-lb woman is legally drunk.

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