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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.

A town's population has been growing linearly. In 2003 the population was 43,000. The population has been growing by 1200 people each year. Write an equation for the population, P, x years after 2003. Use the formula to find the population in 2009.

Learn how to find the equation for a town's linearly growing population. In this example, the population in 2003 was 43,000, growing by 1,200 people annually. Calculate the population for any given year using this linear growth formula. Suitable for students in Grades 8-10.

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