The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is:

To determine the average annual percent increase in the population, we can use the formula for compound annual growth rate (CAGR), which is given by:

\[
\text{CAGR} = \left(\frac{\text{Final Population}}{\text{Initial Population}}\right)^{\frac{1}{n}} - 1
\]

where:
- **Final Population** = 262,500
- **Initial Population** = 175,000
- **n** = number of years (10 years)

1. **Calculate the ratio of the final to the initial population:**

   \[
   \frac{262,500}{175,000} = 1.5
   \]

2. **Calculate the CAGR:**

   \[
   \text{CAGR} = \left(1.5\right)^{\frac{1}{10}} - 1
   \]

   To find \((1.5)^{\frac{1}{10}}\), we can use the approximate value:

   \[
   (1.5)^{\frac{1}{10}} \approx 1.0414
   \]

   So,

   \[
   \text{CAGR} = 1.0414 - 1 = 0.0414 \text{ or } 4.14\%
   \]

Therefore, the average annual percent increase in population is **4.14%**.

Would you like further details or have any questions?

Here are five related questions you might find useful:
1. How is the compound annual growth rate (CAGR) different from simple average growth?
2. Can you calculate the average percent increase if the population grew to 300,000 in the same period?
3. How does population growth affect resource allocation in urban planning?
4. What is the formula for calculating CAGR if the time period is not a whole number?
5. How can population growth models be used to predict future population sizes?

**Tip:** When dealing with percentage increases over time, the compound growth formula is essential to accurately determine the average rate per period.

Learn how to calculate the average annual percent increase in population using compound annual growth rate (CAGR). Given a population increase from 175,000 to 262,500 over a decade, find out the annual percentage growth rate. Includes step-by-step calculation and explanation.

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