2. BLOOD ALCOHOL CONCENTRATION (OPTIMIZATION PROBLEM) Biomedical scientists have studied the chemical and physiological changes in the body that result from alcohol consumption. The reaction in the human body occurs in two stages: a fairly rapid process of absorption and a more gradual one of metabolism. To predict the effect of alcohol consumption, one needs to know the rate at which alcohol is absorbed and metabolized. Medical researchers found that the blood alcohol concentration (BAC) of eight fasting adult male subjects after rapid consumption of 15 mL of ethanol (corresponding to one alcoholic drink) is modeled by the following equation: C(t) = 0.0225te-0.04671 (2) %3D where time t, is measured in minutes after consumption and the concentration C, is measured in mg/mL. Find the maximum value of the BAC during the first hour. Solve the above problem through the following steps: (a) Calculate the first derivative C" (t), of the equation 2. (b) Find C" (t) maximum value of C (t) will occur on interval t = 0, the critical number and then use the first derivative test to find where the (c) Use your answer found in question b to calculate the maximum value of C(t), which is the maximum blood alcohol concentration measured in the first hour.
2. BLOOD ALCOHOL CONCENTRATION (OPTIMIZATION PROBLEM) Biomedical scientists have studied the chemical and physiological changes in the body that result from alcohol consumption. The reaction in the human body occurs in two stages: a fairly rapid process of absorption and a more gradual one of metabolism. To predict the effect of alcohol consumption, one needs to know the rate at which alcohol is absorbed and metabolized. Medical researchers found that the blood alcohol concentration (BAC) of eight fasting adult male subjects after rapid consumption of 15 mL of ethanol (corresponding to one alcoholic drink) is modeled by the following equation: C(t) = 0.0225te-0.04671 (2) %3D where time t, is measured in minutes after consumption and the concentration C, is measured in mg/mL. Find the maximum value of the BAC during the first hour. Solve the above problem through the following steps: (a) Calculate the first derivative C" (t), of the equation 2. (b) Find C" (t) maximum value of C (t) will occur on interval t = 0, the critical number and then use the first derivative test to find where the (c) Use your answer found in question b to calculate the maximum value of C(t), which is the maximum blood alcohol concentration measured in the first hour.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Concept explainers
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Question
Transcribed Image Text:2. BLOOD ALCOHOL CONCENTRATION (OPTIMIZATION PROBLEM)
Biomedical scientists have studied the chemical and physiological changes in the body that result from
alcohol consumption. The reaction in the human body occurs in two stages: a fairly rapid process of
absorption and a more gradlual one of metabolism. To predict the effect of alcohol consumption, one
needs to know the rate at which alcohol is absorbed and metabolized. Medical researchers found that
the blood alcohol concentration (BAC) of eight fasting adult male subjects after rapid consumption of
15 mL of ethanol (corresponding to one alcoholic drink) is modeled by the following equation:
0.04671
C(t) = 0.0225te
(2)
where time t, is measured in minutes after consumption and the concentration C, is measured in
mg/mL. Find the maximum value of the BAC during the first hour.
Solve the above problem through the following steps:
(a) Calculate the first derivative C" (t), of the equation 2.
(b) Find C' (t) = 0, the critical number and then use the first derivative test to find where the
maximum value of C (t) will occur on interval t
(c) Use your answer found in questionb to calculate the maximum value of C'(t), which is the
maximum blood alcohol concentration measured in the first hour.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
