A town has a population of 10000 and grows at 2.5% every year. What will be the population after 7 years, to the nearest whole number?

To find the population of the town after 7 years, given that it grows at a rate of 2.5% per year, we can use the formula for exponential growth:

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

Where:
- \( P(t) \) is the population after time \( t \) years.
- \( P_0 \) is the initial population.
- \( r \) is the growth rate (as a decimal).
- \( t \) is the time in years.

Plugging in the given values:

- \( P_0 = 10,000 \)
- \( r = 2.5\% = 0.025 \)
- \( t = 7 \)

\[
P(7) = 10,000 \times (1 + 0.025)^7
\]

Now, we calculate:

\[
P(7) = 10,000 \times (1.025)^7
\]

\[
P(7) \approx 10,000 \times 1.194
\]

\[
P(7) \approx 11,940
\]

Therefore, the population after 7 years will be approximately **11,940**.

Would you like more details or have any questions?

Here are 8 related questions to consider:
1. What will the population be after 10 years with the same growth rate?
2. How long will it take for the population to double at this growth rate?
3. If the growth rate increases to 3%, what will the population be after 7 years?
4. What is the annual growth rate if the population grows to 12,000 in 7 years?
5. How does the growth rate affect the time it takes for the population to reach 20,000?
6. What would the population be after 7 years if it started at 12,000 instead of 10,000?
7. How does compound interest relate to exponential population growth?
8. How would a 1% annual decrease in population affect the population in 7 years?

**Tip:** When dealing with exponential growth, small changes in the growth rate can lead to significant differences over time.

Learn how to calculate the population of a town after 7 years using the exponential growth formula. Given an initial population of 10,000 growing at a rate of 2.5% per year, discover how to apply the formula P(t) = P0 * (1 + r)^t to find the population after 7 years. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation