Linear Functions: Application
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Transcript of Linear Functions: Application
Linear Functions: Application
Example 1: 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
Linear Functions: Application
a) 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).
2312
2465
2897
5 15102000
2200
2400
2600
2800
3000
Number Of Years Past 1980
En
rollm
ent
Linear Functions: Application
(5, 2312)
(15, 2897)
2897 2312
15 5m
First, use these points and the slope formula to find the slope of the line.
585
10
58.5
Linear Functions: Application
Substitute one of the points and slope into the point-slope equation, y – y1 = m(x – x1), to get:
y – 2312 = 58.5(x – 5).
(5, 2312)
(15, 2897)
58.5m
Linear Functions: Application
Next, put y – 2312 = 58.5(x – 5) in slope-intercept form.
y – 2312 = 58.5x – 292.5
y = 58.5x + 2019.5
Linear Functions: Application
b) Use 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.
Linear Functions: Application
Try: 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
Linear Functions: Application
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.
Linear Functions: Application