Hey, GPT.
Could you help me solve this word problem? I'm stuck on it and could use some help:

"If a town with a population of 3,000 grows by 2% per year, how large will the population be in ten years?"

Certainly! This is a problem involving exponential growth, and the general formula for this type of problem is:

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

Where:
- \(P(t)\) is the population after time \(t\),
- \(P_0\) is the initial population,
- \(r\) is the growth rate per time period (as a decimal),
- \(t\) is the number of years.

From the problem:
- The initial population \(P_0 = 3000\),
- The growth rate \(r = 2\% = 0.02\),
- The time period \(t = 10\) years.

Now, substitute these values into the formula:

\[
P(10) = 3000 \times (1 + 0.02)^{10}
\]

\[
P(10) = 3000 \times (1.02)^{10}
\]

Now calculate \( (1.02)^{10} \):

\[
(1.02)^{10} \approx 1.21899
\]

Thus, the population after 10 years is approximately:

\[
P(10) = 3000 \times 1.21899 \approx 3657
\]

So, the population will be about **3,657** after 10 years.

Would you like further clarification or details on any step? Here are some additional questions to help explore this further:

1. How would the population change if the growth rate were 3% instead of 2%?
2. What would the population be after 5 years, using the same growth rate?
3. How does the growth rate influence the long-term population size?
4. What is the concept behind exponential growth, and how is it different from linear growth?
5. How can you apply this type of formula to other real-life situations, such as money in a bank account?

**Tip:** When working with percentages in formulas, remember to convert the percentage to a decimal (e.g., 2% becomes 0.02) before using it in calculations.

If a town with a population of 3,000 grows by 2% per year, how large will the population be in ten years?

Learn how to calculate the population of a town growing at 2% per year using the exponential growth formula. This step-by-step solution covers key algebraic concepts and percentage growth, making it ideal for students in Grades 8-10.

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