A town has a population of 12000 and grows at 5% every year. What will be the population after 12 years, to the nearest whole number?

To calculate the population after 12 years, we can use the formula for exponential growth:

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

Where:
- \(P(t)\) is the population after \(t\) years,
- \(P_0\) is the initial population (12,000),
- \(r\) is the annual growth rate (5% or 0.05),
- \(t\) is the number of years (12).

Substituting the values:

\[
P(12) = 12,000 \times (1 + 0.05)^{12}
\]

\[
P(12) = 12,000 \times (1.05)^{12}
\]

Now, calculating:

\[
P(12) \approx 12,000 \times 1.795856
\]

\[
P(12) \approx 21,550
\]

So, the population after 12 years will be approximately 21,550.

Would you like further explanation on this?

Here are 5 related questions:
1. What would the population be after 20 years with the same growth rate?
2. How would the population change if the growth rate were 3% instead of 5%?
3. How does compound interest relate to this type of population growth?
4. Can the exponential growth formula be used for non-annual growth rates?
5. How long would it take for the population to double at a 5% growth rate?

**Tip:** Exponential growth can rapidly increase numbers over time due to the effect of compounding, so small annual percentages make a big difference over long periods.

Discover how to calculate the population of a town after 12 years of 5% annual growth, using the exponential growth formula. Starting with 12,000 people, the town's population grows to approximately 21,550. This example demonstrates key concepts of exponential growth and compounding.

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