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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 6DE
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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.
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