A town has a population of 13000 and grows at 2.5% every year. What will be the population after 5 years, to the nearest whole number?

To calculate the population after 5 years with an annual growth rate of 2.5%, 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 (13,000 in this case).
- \( r \) is the growth rate (2.5% or 0.025).
- \( t \) is the number of years (5 years in this case).

Substitute the given values into the formula:

\[
P(5) = 13000 \times (1 + 0.025)^5
\]

Now, calculate:

\[
P(5) = 13000 \times (1.025)^5
\]

\[
P(5) = 13000 \times 1.1314 \approx 14708.2
\]

To the nearest whole number, the population after 5 years will be approximately **14,708**.

Would you like further details or explanations on this calculation?

Here are some related questions:
1. How does the exponential growth formula change with different growth rates?
2. What if the growth rate changes after 3 years? How would you recalculate?
3. How does this population growth compare to linear growth?
4. What would the population be after 10 years at the same rate?
5. How would decreasing the growth rate to 1% affect the 5-year population projection?

**Tip:** Always ensure to express percentages as decimals when applying them in formulas (e.g., 2.5% becomes 0.025).

Learn how to calculate the population growth of a town with an initial population of 13,000 and a 2.5% annual growth rate. This step-by-step solution shows how to apply the exponential growth formula to determine the population after 5 years. Suitable for students in Grades 9-12.

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