https://file.aiquickdraw.com/mathbot/file/1729129260692ketomoj0.jpg

The problem in the image asks about a town with an initial population of 1,000 people that grows by 12% per year, and it seeks to determine the population after 9 years.

This is a problem of exponential growth, which can be modeled by the formula:

\[
P(t) = P_0 (1 + r)^t
\]

Where:
- \( P(t) \) is the population after \( t \) years.
- \( P_0 \) is the initial population (1,000 people).
- \( r \) is the growth rate per year (12% or 0.12).
- \( t \) is the number of years (9 years).

Substituting the given values:

\[
P(9) = 1000 \times (1 + 0.12)^9 = 1000 \times (1.12)^9
\]

Let's calculate:

\[
P(9) \approx 1000 \times 2.773 = 2773 \text{ people}
\]

So, after 9 years, the population will be approximately **2,773** people.

Would you like more details on the calculation or have any questions?

Here are some related questions to consider:
1. What would happen if the growth rate increased to 15%?
2. How would the population change over 15 years instead of 9?
3. How does exponential growth differ from linear growth?
4. What is the doubling time for this population with a 12% growth rate?
5. How would the population be affected if there was a migration of 200 people out every year?

**Tip:** Exponential growth compounds over time, meaning small percentage increases can lead to large changes in the long term.

A town has a population of 1000 people and is increasing by 12% each year. What will the population be at the end of 9 years?

This problem involves calculating the population of a town growing at a rate of 12% per year, starting with 1,000 people. Learn how to apply exponential growth formulas to find the population after 9 years, suitable for students in Grades 8-10.

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