This problem describes a linear growth in population. Let's break it down:

Step 1: Writing the equation for population

• The population in 2003 was 46,000.
• Each year, the population increases by 1,700 people.

The general form of a linear equation is:

$P = P_0 + r \cdot x$

Where:

• $P_0$ is the initial population (in 2003), which is 46,000.
• $r$ is the rate of change (increase per year), which is 1,700.
• $x$ is the number of years after 2003.

Thus, the equation becomes:

$P = 46000 + 1700 \cdot x$

Step 2: Finding the population in 2009

To find the population in 2009, calculate the number of years after 2003:

$x = 2009 - 2003 = 6$

Substitute $x = 6$ into the equation:

$P = 46000 + 1700 \cdot 6$

Now, calculate the result:

$P = 46000 + 10200 = 56,200$

Thus, the population in 2009 is 56,200.

Would you like a detailed explanation or further clarification on any part of this?

Here are five related questions for practice:

1. What would the population be in 2015?
2. How many years will it take for the population to reach 80,000?
3. If the population growth rate changed to 2,000 per year, how would the equation change?
4. What is the population growth rate per month based on the yearly increase?
5. If the initial population was 50,000 in 2003, how would the equation change?

Tip: In linear models, the slope (rate of change) shows how quickly values increase or decrease per unit of time.