A town has 7,534 people in 2006 and grows at the rate of 3% per year. How many people will live in this town in 2023?

The population growth in this case follows the formula for exponential growth:

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

Where:
- \(P(t)\) is the population at time \(t\).
- \(P_0\) is the initial population.
- \(r\) is the growth rate per year (expressed as a decimal).
- \(t\) is the number of years from the starting point.

Here:
- \(P_0 = 7,534\)
- \(r = 0.03\) (since 3% growth rate)
- \(t = 2023 - 2006 = 17\) years

Now, applying the formula:

\[
P(17) = 7,534 \times (1 + 0.03)^{17}
\]

Let's calculate that.The projected population of the town in 2023 is approximately 12,453 people.

Would you like further details or have any questions?

Here are five related questions:
1. How would the population change if the growth rate was 5% instead of 3%?
2. How long will it take for the population to double at a 3% growth rate?
3. What would the population be in 2030 at the same growth rate?
4. How would the calculation differ if the growth rate were decreasing over time?
5. How would the formula change if the population grew linearly instead of exponentially?

**Tip:** In exponential growth problems, small differences in growth rates can lead to large changes over long periods!

Learn how to calculate the population growth of a town from 7,534 people in 2006 to 2023, growing at 3% per year. This solution involves exponential growth concepts and the formula P(t) = P_0 × (1 + r)^t, with detailed step-by-step calculations. Suitable for Grades 9-12 students.

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