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 FunctionThe human immunodeficiency virus, or HIV, infects and kills helper T cells. BecauseT cells stimulate the immune system to produce antibodies, their destructiondisables the body's defenses against other pathogens. By counting the number ofT 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 graphthat is used to monitor the average progression of the disease. The average numberof T cells, f(x), is a function of time after infection, x.yT Cell Count and HIV Infection1200Asymptomatic StageFew or no symptoms present.1000800Symptomatic StageSymptoms begin or* 600get worse.AIDS ClinicalDiagnosis400200y = flx)1 23 4 5 6 7 86.10 11Time after Infection (years)FIGURE 2.9Source: 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)

From the graph shown in the figure. At x = 5 the y coordinate is 400. Hence f(5) = 400

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

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Concept explainers

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.

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)

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