Question: There were 50 software companies in Smart City Software Park in the year 2000. Subsequently, the number of software companies increased by 20 each year. Write a linear model for the number of software companies. What could be the number in the year 2008? A )
l = 20
t + 50, 210
B )
l = 20(
t + 50), 160
C )
l = 20
t - 50, 220
D )
l = 50
t - 20, 195
Steps to derive 1 Let
l be the variable representing the number of software companies and
t be the variable representing the number of years.
2 The slope is the rate at which software companies increases in number = 20
3 t = 0 represents the year 2000. So,
t = 1 represents the year 2001.
4 In the year 2000, the number of software companies is 50.
5 (
t 1 ,
l 1 ) = (0, 50) is a point on the line whose slope is 20.
6 The equation of the line passing through the point (
t 1 ,
l 1 ) with slope
m in point-slope form is
l -
l 1 =
m (
t -
t 1 ).
[Substitute
t 1 = 0,
l 1 = 50 and
m = 20.]
7 l - 50 = 20(
t - 0)
[Distribute 20.]
8 l - 50 = 20
t [Add 50 to both sides.]
9 l = 20
t + 50
10 The linear model for the number of software companies in the year 2008 is
l = 20
t + 50
11 t = 8 represents the year 2008.
[Substitute
t = 8 in the linear model.]
12 l = 20(8) + 50
[Simplify.]
13 l = 210
14 The number of software companies in the year 2008 in Smart City Software Park is 210.
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