Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

After an antibiotic taken is taken, the concentra…

01:45

Question

Answered step-by-step

Problem 69 Hard Difficulty

After the consumption of an alcoholic beverage, the concentration of alcohol in the bloodstream (blood alcohol concentration, or BAC) surges as the alcohol is absorbed, followed by a gradual decline as the alcohol is metabolized. The function

$$ C(t) = 1.35te^{-2.802t} $$

models the average BAC, measured in mg/mL, in a group of eight male subjects $t$ hours after rapid consumption of $15$ ml of ethanol (corresponding to one alcoholic drink). What is the maximum average BAC during the first $3$ hours? When does it occur?

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.


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Leon Druch
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Leon Druch

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

More Answers

03:06

WZ

Wen Zheng

01:24

Amrita Bhasin

08:29

Mutahar Mehkri

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 1

Maximum and Minimum Values

Related Topics

Derivatives

Differentiation

Volume

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Kayleah Tsai

Harvey Mudd College

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

Calculus 2 / BC Courses

Lectures

Video Thumbnail

04:35

Volume - Intro

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

Video Thumbnail

06:14

Review

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

Join Course
Recommended Videos

0:00

After the consumption of a…

02:44

After the consumption of a…

03:23

After an alcoholic beverag…

03:35

After the consumption of a…

07:07

After an alcoholic beverag…

11:15

After an alcoholic beverag…

05:38

After the consumption of a…

04:39

After the consumption of a…

01:20

Blood alcohol concentratio…

01:33

Blood alcohol concentratio…

01:07

The average blood alcohol …

04:15

The average blood alcohol …

04:20

Blood alcohol concentratio…

02:37

Researchers measured the b…

12:35

Blood alcohol concentratio…

02:13

Blood alcohol content (BAC…

0:00

After alcohol is fully abs…

Watch More Solved Questions in Chapter 4

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80

Video Transcript

here we have a function C. F. T equals 1.35 times T times E. To the negative 2.8 oh two times T. Power. Uh C. Represents the blood alcohol concentration. Uh And it is a function of t uh The number of hours. And we want to find uh what is the maximum blood alcohol concentration during the first three hours? And exactly at what value of T. Uh You know, what exact number of hours does it occur? So here is C. As a function of T. And uh for uh the interval between zero and three the first three hours, we want to find out when this function, this blood alcohol concentration function has a maximum. Uh So we could do it two ways. You could find the derivative of this function with respect to T. Set that derivative equal to zero and solve that equation. 40. And the value of T. Uh That makes us the first derivative equal to zero. Um At that value of T. Where the first derivative become zero. You have either a local maximum or local minimum. So this is one way where you can find uh the maximum value of the uh c. Of T function by setting the first derivative equal to zero. Um We are going to take a graphing approach. So we're going to use dez most graphing calculator input. This function and look for the maximum on the graph. So here is the blood alcohol concentration function uh entered. And this blue curve is the graph of the blood alcohol uh concentration to cfx function. You can see in the end of role. Um Now the only difference was I had to use using Dismas instead of using T. For hours. I'm using the variable X. For hours. But you can see on the end of all, between zero hours and three hours, our sea of X function does reach a maximum point right here. Um So during the first three hours the blood alcohol concentration does reach a maximum the time. Okay? The X coordinate the T coordinate at T equals 0.357 hours. Uh Our function reaches a maximum at T equals 0.357 hours. Uh We have the maximum blood alcohol concentration and that maximum Blood alcohol concentration is .177. And that is measured in milligrams per mm. So at .357 hours the blood alcohol concentration reaches a maximum a .177 milligrams per milliliters.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
126
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
62
Hosted by: Alonso M
See More

Related Topics

Derivatives

Differentiation

Volume

Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Kayleah Tsai

Harvey Mudd College

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

Calculus 2 / BC Courses

Lectures

Video Thumbnail

04:35

Volume - Intro

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

Video Thumbnail

06:14

Review

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

Join Course
Recommended Videos

0:00

After the consumption of an alcoholic beverage, the concentration of alcohol in…

02:44

After the consumption of an alcoholic beverage, the concentration of alcohol in…

03:23

After an alcoholic beverage is consumed, the concentration of alcohol in the bl…

03:35

After the consumption of an alcoholic beverage, the concentration of alcohol in…

07:07

After an alcoholic beverage is consumed the concentration of alcohol in the blo…

11:15

After an alcoholic beverage is consumed, the concentration of alcohol in the bl…

05:38

After the consumption of an alcoholic beverage, the concentration of alcohol in…

04:39

After the consumption of an alcoholic beverage the concentration of alcohol in …

01:20

Blood alcohol concentration In Section 3.1 we modeled the BAC of male adult sub…

01:33

Blood alcohol concentration Researchers measured the blood alcohol concentratio…

01:07

The average blood alcohol concentration (BAC) of eight male subjects was measur…

04:15

The average blood alcohol concentration (BAC) of eight male subjects was measur…

04:20

Blood alcohol concentration Researchers measured the blood alcohol concentratio…

02:37

Researchers measured the blood alcohol concentration (BAC) of eight adult male …

12:35

Blood alcohol concentration After alcohol is fully absorbed into the body, it i…

02:13

Blood alcohol content (BAC) is sometimes reported in weight-volume percent and,…

0:00

After alcohol is fully absorbed into the body, it is metabolized. Suppose that …
Additional Mathematics Questions

01:00

A firm is offered trade credit of 1/5, net 15. If the firms pays
on day 2…

05:04

The temperature during a day can be modeled by a sinusoid.
Answer the fol…

02:21

x^2 (x+1) (x-8) > 0
Set one side equal to zero and list the interval e…

03:21

Write the equation 9𝑥 2 − 𝑦 2 − 14𝑦 − 58 = 0 in standard form
and determi…

01:23

If the depth of water in a basin is x cm, the volume is
30x(10+2x)cm^3. …

01:40

The population of a city is modeled by the equation
P(t)=249,246e0.15t wh…

03:21

A ferris wheel is 35 meters in diameter and boarded from a
platform that …

01:03

Write the following function in terms of its cofunction.
cos(π/8) Write y…

13:43


Find the x-intercepts of each of the following functions. Also, describe…

03:54

7: Find the accumulated amount A if the
principal P is invested at the in…

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started