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

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

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.

Problem

After an antibiotic taken is taken, the concentra…

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

More Answers

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 2 / BC Educators

Catherine Ross

Kayleah Tsai

Samuel Hannah

Michael Jacobsen

Calculus 2 / BC Courses

Recommended Videos

Watch More Solved Questions in Chapter 4

Video Transcript

James Stewart

Calculus: Early Transcendentals

Catherine Ross

Kayleah Tsai

Samuel Hannah

Michael Jacobsen

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

Calculus: Early Transcendentals

Catherine Ross

Kayleah Tsai

Samuel Hannah

Michael Jacobsen

James StewartCalculus: Early Transcendentals

Catherine Ross

Kayleah Tsai

Samuel Hannah

Michael Jacobsen

James Stewart

Calculus: Early Transcendentals