Linear equations Word Problems

Question

Abbivlle is a small town that has been steadily growing since 1960.use the table below to create a linear equation that estimates Abbivlle's population over time. What will the population be in 2016 if the growth remains constant?

Year-       (1960) (1970) (1980) (1990) (2000)
Population- (60)    (76)    (92)    (108)   (124)

Answer 1

Notice that the difference in population every 10 years is the same, 16.

 

This means the linear equation will have a slope of

 

m = rise/run = 16/10 = 1.6 .

 

If x represents the number of years after 1960, then

 

1960 corresponds to x = 0,

1970 corresponds to x = 10,

 

etc.

 

This means, that the y-intercept is the population in 1960, or 60. b = 60, m = 1.6 leads to the equation

 

y = 1.6x + 60.

 

To check, put x = 40 (the year 2000) in this equation and calculate y = 64 + 60 = 124. OK!