Question 0.1.15: Using a Line to Predict Population From the population data ...
Using a Line to Predict Population
From the population data for the census years 1960, 1970, 1980 and 1990 given in example 1.8, predict the population for the year 2000.
We began this subsection by showing that the points in the corresponding table are not colinear. Nonetheless, they are nearly colinear. So, why not use the straight line connecting the last two points (20, 227) and (30, 249) (corresponding to the populations in the years 1980 and 1990) to predict the population in 2000? (This is a simple example of a more general procedure called extrapolation.) The slope of the line joining the two data points is
m=\frac{249-227}{30-20}=\frac{22}{10}=\frac{11}{5}The equation of the line is then
y=\frac{11}{5}(x-30)+249.
See Figure 0.17 for a graph of the line. If we follow this line to the point corresponding to x = 40 (the year 2000), we have the predicted population
\frac{11}{5}(40-30)+249=271.
That is, the predicted population is 271 million people. The actual census figure for 2000 was 281 million, which indicates that the U.S. population grew at a faster rate between 1990 and 2000 than in the previous decade.
