To solve this problem, let's break it down step by step.

Step 1: Write the equation for the population

The population is growing linearly, which means we can use a linear equation of the form:

$P(t) = P_0 + rt$

Where:

• $P(t)$ is the population at time $t$ years after 2000.
• $P_0$ is the initial population at $t = 0$ (which is the population in the year 2000).
• $r$ is the rate of population growth per year.
• $t$ is the number of years after 2000.

From the problem:

• $P_0 = 25,000$ (the population in 2000)
• $r = 1,200$ people per year
• $t$ is the number of years after 2000

Thus, the equation for the population $t$ years after 2000 is:

$P(t) = 25,000 + 1,200t$

Step 2: Find the population in 2009

To find the population in 2009, note that 2009 is 9 years after 2000, so $t = 9$.

Substitute $t = 9$ into the equation:

$P(9) = 25,000 + 1,200 \times 9$ $P(9) = 25,000 + 10,800$ $P(9) = 35,800$

Final Answer:

• The equation for the population $t$ years after 2000 is: $P(t) = 25,000 + 1,200t$
• The population in 2009 is $35,800$.

Would you like further details on any of the steps? Here are some related questions you might find interesting:

1. What would the population be in 2020 using the same formula?
2. How would the formula change if the population were growing exponentially instead of linearly?
3. What is the population increase from 2005 to 2009?
4. If the growth rate changed to 1,500 people per year starting in 2010, how would the equation change?
5. How would the equation be affected if there was a decrease in population starting in 2015?

Tip: When dealing with linear growth problems, remember that the slope (rate of change) represents the amount of change per unit time.