Question

A town's population has been growing linearlyIn 2003 the population was 21, 000 . The population has been growing by 2200 people each year. Write an equation for the population , P, x years after 2003 .P=Use the formula to find the population in 2009

Answer 1

P = 2200x + 21000

Population in 2009: 34200

Explanation

Variables

• x: number of years after 2003

,

• P: population

The relation between these variables is linear, then they can be related by the next formula:

`P=mx+b`

where m is the slope and (0, b) is the y-intercept of the line

In the year 2003, the x-variable has a value of zero and a population of 21,000. Therefore, the line passes through the point (0, 21000). This means that b = 21,000.

Given that the population has been growing by 2200 people per year, then the slope of the line is m = 2200

Substituting m = 2200 and b = 21,000 into the general formula:

`P=2200x+21000`

In the year 2009, the x-variable has the next value:

`\begin{gathered} x=2009-2003 \\ x=6 \end{gathered}`

Substituting x = 6 into the previous formula:

`\begin{gathered} P=2200*6+21000 \\ P=13200+21000 \\ P=34200 \end{gathered}`