We are given the following information:

• The town's population in 2003 was 43,000.
• The population has been growing by 1,200 people each year.

1. Writing the Equation:

We need to express the population $P$ as a function of $x$, where $x$ represents the number of years after 2003.

The general equation for linear growth is:

$P = P_0 + r \cdot x$

Where:

• $P_0$ is the initial population (in 2003, this was 43,000),
• $r$ is the rate of growth per year (1,200 people),
• $x$ is the number of years after 2003.

So, the equation becomes:

$P = 43000 + 1200x$

2. Finding the Population in 2009:

To find the population in 2009, we need to substitute $x = 2009 - 2003 = 6$ into the equation.

$P = 43000 + 1200 \cdot 6$

Now, calculating the population:

$P = 43000 + 7200 = 50200$

So, the population in 2009 is 50,200.

Would you like further explanation or details on how this was solved?

Relative Questions:

1. How do you derive the slope for linear population growth models?
2. What happens if the population decreases by a certain amount each year?
3. How would the equation change if the town started with a different population in 2003?
4. Can the population growth be modeled using an exponential function instead of a linear one?
5. How would you calculate the population in any future year using this formula?

Tip:

Always double-check units (years, people, rates) to ensure consistency when plugging values into the formula.