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Linear Functions: Application

The fall enrollment figures at a community college are shown.

2312

2465

2897

5 15102000

2200

2400

2600

2800

3000

Number Of Years Past 1980

En

rollm

ent

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Linear Functions: Application

Slide 2

Use the figures only for 1985 and 1995 to write a linear model (function) for the enrollment, y, in terms of the number of years past 1980, x.

The point for 1985 is (5, 2312). The point for 1995 is (15, 2897).

.5.5810585

51523122897

m

First, use these points and the slope formula to find the slope of the line.

Substitute one of the points and slope into the point-slope equation, y – yc = m(x – xc), to get:

y – 2312 = 58.5(x – 5).

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Linear Functions: Application

Slide 3

Next put, y – 2312 = 58.5(x – 5) in slope-intercept form. y – 2312 = 58.5x – 292.5

y = 58.5x + 2019.5Use the linear model to predict the enrollment in 2010.

The year 2010 corresponds to x = 30 (30 years after 1980). Substitute this into the linear model to get:

y = 58.5(30) + 2019.5 = 3774.5

According to the model, the enrollment in 2010 will be 3775 students.

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Linear Functions: Application

Slide 4

The population of a small town for selected years is shown.

20896

22350

23104

3 9 620000

21000

22000

23000

24000

25000

Number Of Years Past 1990

Po

pu

lati

on

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Linear Functions: Application

Slide 5

Use the figures only for 1993 and 1999 to write a linear model (function) for the town's population, y, in terms of the number of years past 1990, x.

Use the linear model to predict the town's population in 2010.

y = 368x + 19792

According to the model, the town's population in 2010 will be 27,152.

Table of Contents

Linear Functions: Application