To solve this linear population modeling problem, let's break it down:

Problem:

• In 2003, the population was 68,000.
• The population grows by 1,700 people per year.
• We are tasked to write an equation for the population, $P$, after $x$ years from 2003.

1. Writing the Equation

The population growth is linear, which follows the form of the equation: $P = P_0 + r \cdot x$ Where:

• $P_0$ is the initial population (in 2003, this is 68,000),
• $r$ is the rate of population growth per year (1,700 people per year),
• $x$ is the number of years after 2003.

So, the equation becomes: $P = 68,000 + 1,700 \cdot x$

2. Finding the Population in 2009

Now, to find the population in 2009, we need to determine the number of years between 2003 and 2009: $x = 2009 - 2003 = 6 \text{ years}$

Substitute $x = 6$ into the equation: $P = 68,000 + 1,700 \cdot 6$ $P = 68,000 + 10,200 = 78,200$

Thus, the population in 2009 is 78,200.

Final Answers:

• Equation: $P = 68,000 + 1,700 \cdot x$
• Population in 2009: $78,200$

Would you like further details or have any questions?

Related Questions:

1. What would the population be in 2015 according to this model?
2. How many years will it take for the population to reach 100,000 people?
3. What happens to the equation if the population growth rate increases to 2,000 people per year?
4. If the population starts decreasing by 1,700 people per year instead of increasing, what would the equation look like?
5. What is the significance of the slope in this linear model in terms of population growth?

Tip:

In linear models, the slope (rate of change) indicates how much the dependent variable (population) changes for each unit increase in the independent variable (years).