Question

Try It #2

A city’s population has been growing linearly. In 2008, the population was 28,200. By 2012, the population was36,800. Assume this trend continues.
a. Predict the population in 2014

Answer 1

The population in year 2014 is 41100.

Explanation:

In the question, it is given that the city's population is growing linearly. In 2008 , population was 28200 and in 2012 , it is 36800 .

It is required to predict the population in 2014 .

To do so, use the population given in two years as two points on a line and find the equation of population and year. Then, find the population in year 2014 .

Step 1 of 2

The population in 2008 was 28200 and in 2012 it was, 36800 .

The equation relating population and year is,

`$$\begin{aligned}&y-28200=\left((36800-28200)/(2012-2008)\right)(x-2008) \\&y-28200=\left((8600)/(4)\right)(x-2008) \\&y-28200=2150(x-2008)\end{aligned}$$`

Step 2 of 2

The population in year 2014 can be determined by substituting 2014 for x,

`$$\begin{aligned}&y-28200=2150(2014-2008) \\&y-28200=2150(6) \\&y-28200=12900 \\&y=41100\end{aligned}$$`