Question

A town's population has been growing linearly. In 2003 the population was 36,000. The population has been growing by 700 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

To write the equation for the population \( P \) as a function of the number of years \( x \) after 2003, we can use the information given:

- In 2003 (which we can consider as \( x = 0 \)), the population \( P = 36,000 \).
- The population is increasing by 700 people each year.

The equation can be written in the form:

\[
P = P_0 + r \cdot x
\]

where:
- \( P_0 \) is the initial population,
- \( r \) is the growth rate (in people per year),
- \( x \) is the number of years after 2003.

Substituting the known values into the equation:

\[
P = 36,000 + 700x
\]

Now, to find the population in 2009, we calculate \( x \):

\[
x = 2009 - 2003 = 6
\]

Now substituting \( x = 6 \) into the population equation:

\[
P = 36,000 + 700 \times 6
\]

Calculating the value:

\[
P = 36,000 + 4,200
\]
\[
P = 40,200
\]

So, the population in 2009 is **40,200**.