y T Cell Count and HIV Infection 1200 Asymptomatic Stage Few or no symptoms present. 1000 800 Symptomatic Stage Symptoms begin or get worse. 600 400 AIDS Clinical Diagnosis 200 y = f(x) 1 2 3 4 6 7 8 9 10 11 Time after Infection (years) Average T Cell Count (per milliliter of blood)
y T Cell Count and HIV Infection 1200 Asymptomatic Stage Few or no symptoms present. 1000 800 Symptomatic Stage Symptoms begin or get worse. 600 400 AIDS Clinical Diagnosis 200 y = f(x) 1 2 3 4 6 7 8 9 10 11 Time after Infection (years) Average T Cell Count (per milliliter of blood)
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.EA: Extended Application Using Extrapolation To Predict Life Expectancy
Problem 6EA
Related questions
Question
1. Use the graph to find f(5)
2. What is the value of x when f(x) =100?
![EXAMPLE 7 Analyzing the Graph of a Function
The human immunodeficiency virus, or HIV, infects and kills helper T cells. Because
T cells stimulate the immune system to produce antibodies, their destruction
disables the body's defenses against other pathogens. By counting the number of
T cells that remain active in the body, the progression of HIV can be monitored.
The fewer helper T cells, the more advanced the disease. Figure 2.9 shows a graph
that is used to monitor the average progression of the disease. The average number
of T cells, f(x), is a function of time after infection, x.
y
T Cell Count and HIV Infection
1200
Asymptomatic Stage
Few or no symptoms present.
1000
800
Symptomatic Stage
Symptoms begin or
* 600
get worse.
AIDS Clinical
Diagnosis
400
200
y = flx)
1 2
3 4 5 6 7 8
6.
10 11
Time after Infection (years)
FIGURE 2.9
Source: B. E. Pruitt et al., Human Sexuality, Prentice Hall, 2007.
a. Explain why f represents the graph of a function.
b. Use the graph to find and interpret f(8).
c. For what value of x is f(x) = 350?
d. Describe the general trend shown by the graph.
Average T Cell Count
(per milliliter of blood)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbebe69f5-2538-465a-ba20-2a88330e8d3f%2F8c837018-865f-4b09-9e12-d9b6799b99a8%2Fwxezfjm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:EXAMPLE 7 Analyzing the Graph of a Function
The human immunodeficiency virus, or HIV, infects and kills helper T cells. Because
T cells stimulate the immune system to produce antibodies, their destruction
disables the body's defenses against other pathogens. By counting the number of
T cells that remain active in the body, the progression of HIV can be monitored.
The fewer helper T cells, the more advanced the disease. Figure 2.9 shows a graph
that is used to monitor the average progression of the disease. The average number
of T cells, f(x), is a function of time after infection, x.
y
T Cell Count and HIV Infection
1200
Asymptomatic Stage
Few or no symptoms present.
1000
800
Symptomatic Stage
Symptoms begin or
* 600
get worse.
AIDS Clinical
Diagnosis
400
200
y = flx)
1 2
3 4 5 6 7 8
6.
10 11
Time after Infection (years)
FIGURE 2.9
Source: B. E. Pruitt et al., Human Sexuality, Prentice Hall, 2007.
a. Explain why f represents the graph of a function.
b. Use the graph to find and interpret f(8).
c. For what value of x is f(x) = 350?
d. Describe the general trend shown by the graph.
Average T Cell Count
(per milliliter of blood)
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
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
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Calculus For The Life Sciences](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
![Glencoe Algebra 1, Student Edition, 9780079039897…](https://www.bartleby.com/isbn_cover_images/9780079039897/9780079039897_smallCoverImage.jpg)
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Calculus For The Life Sciences](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
![Glencoe Algebra 1, Student Edition, 9780079039897…](https://www.bartleby.com/isbn_cover_images/9780079039897/9780079039897_smallCoverImage.jpg)
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781938168383/9781938168383_smallCoverImage.gif)