Linear Application Problems

Question

The population of a small town in central Florida has shown a linear decline in the years 1992-2002. In 1992 the population was 31000 people. In 2002 it was 22000 people.

A) Write a linear equation expressing the population of the town, P, as a function of t, the number of years since 1992.

B) If the town is still experiencing a linear decline, what will the population be in 2006?

Answer 1

A linear equation can be written in slope-intercept form (y-mx+b). To find the slope (m), we need 2 points.If we say 1992 is x=0, we have the point (0,31000) and (10,22000) for 2002.

Slope is defined by the change in the y-values divided by the change in the x-values. Some call it "rise over run".

Change in y-values: 22000-31000 = -9000

Change in x-values: 10 - 0 = 10

slope: -9000/10 = -900 - This means the population decreases by 900 each year.

So now we have y = -900x + b

b is the y-value when x is 0. we already know that to be 31000.

y = -900x + 31000

To solve for the population in 2006 (14 years after 1992), we plug in 14 for x.

y = -900 *14 + 31000

y = -12600 + 31000 - the population has decreased by 12,600

y = 18,400 - this is the population in 2006