The town's population is growing linearly, meaning the population can be modeled by a linear function. The general form of a linear function is:

$P(t) = P_0 + rt$

Where:

• $P(t)$ is the population at time $t$ (years after 2003),
• $P_0$ is the population at $t = 0$ (i.e., the population in 2003),
• $r$ is the rate of population growth per year,
• $t$ is the number of years after 2003.

From the problem:

• In 2003, the population was 62,400 people, so $P_0 = 62,400$.
• The population grows by 3,600 people each year, so $r = 3,600$.

Thus, the function that models the population $P(t)$ is:

$P(t) = 62,400 + 3,600t$

Finding the population in 2015:

2015 is 12 years after 2003, so $t = 12$. Substitute $t = 12$ into the function:

$P(12) = 62,400 + 3,600 \times 12$

$P(12) = 62,400 + 43,200$

$P(12) = 105,600$

Conclusion:

In 2015, the population of the town will be 105,600 people.

Would you like further details or have any questions?

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Here are 5 related questions you might find interesting:

1. What would the population be in the year 2020 using this model?
2. How long will it take for the population to reach 150,000 people?
3. If the growth rate changed after 2015 to 4,500 people per year, how would the formula change?
4. What is the population change between 2003 and 2010?
5. How would a decrease in population by 1,200 per year after 2015 affect the population in 2020?

Tip: Linear models assume a constant rate of change. For more complex scenarios, exponential or logistic models might be more accurate.