The average blood alcohol concentration (BAC) of eight male subjects was measured after consumption of 15 mL of ethanol (corresponding to one alcoholic drink). The resulting data were modeled by the concentration function
C(t) = 0.0225te–0.0467t
where t is measured in minutes after consumption and C is measured in mg/mL.
(a) How rapidly was the BAC increasing after 10 minutes?
(b) How rapidly was it decreasing half an hour later?
Source: Adapted from P. Wilkinson et al., “Pharmacokinetics of Ethanol after Oral Administration in the Fasting State,” Journal of Pharmacokinetics and Biopharmauutics5 (1977): 207- 24.
To find: The increase in BAC after 10 minutes.
The resulting data the modeled by the concentration function .
(1) Product Rule:
Result used: Chain Rule
If g is differentiable at t and f is differentiable at , then the composite function defined by is differentiable at t and is given by the product
Obtain the derivative .
Apply the product rule (1),
To find: The decrease in BAC half an hour later.
Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!Get Started
Calculus: Early Transcendental Functions
Calculus: An Applied Approach (MindTap Course List)
Finite Mathematics and Applied Calculus (MindTap Course List)
Single Variable Calculus: Early Transcendentals, Volume I
Precalculus: Mathematics for Calculus (Standalone Book)
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Essentials Of Statistics
Calculus (MindTap Course List)
Statistics for The Behavioral Sciences (MindTap Course List)
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Single Variable Calculus
Understanding Basic Statistics
Probability and Statistics for Engineering and the Sciences
Contemporary Mathematics for Business & Consumers
Elementary Geometry For College Students, 7e
Mathematical Applications for the Management, Life, and Social Sciences
Mathematical Excursions (MindTap Course List)
Elementary Technical Mathematics
Single Variable Calculus: Early Transcendentals
Calculus of a Single Variable
Calculus: Early Transcendental Functions (MindTap Course List)
Elements Of Modern Algebra
Trigonometry (MindTap Course List)
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Study Guide for Stewart's Multivariable Calculus, 8th
Elementary Geometry for College Students
Finite Mathematics for the Managerial, Life, and Social Sciences