In​ 2001, the population in a town was 9​% more than it was in 2000. If the population was 24 comma 930 in​ 2002, which was​ 10% more than​ 2001, find the population in 2000. 

To find the population of the town in 2000, let's break down the problem step by step. We know the population in 2002 and the percentage increases for each year.

### Given Information:
1. Population in 2001 was 9% more than in 2000.
2. Population in 2002 was 10% more than in 2001.
3. Population in 2002 is given as 24,930.

### Let's Define Variables:
- Let \( P_{2000} \) be the population in the year 2000.
- Population in 2001 is \( P_{2001} = P_{2000} \times 1.09 \).
- Population in 2002 is \( P_{2002} = P_{2001} \times 1.10 \).

### Step-by-Step Calculation:

1. **Find the relationship between the populations of 2002 and 2000:**

   Since \( P_{2002} = P_{2001} \times 1.10 \) and \( P_{2001} = P_{2000} \times 1.09 \), we can substitute for \( P_{2001} \) in the equation for \( P_{2002} \):

   \[
   P_{2002} = (P_{2000} \times 1.09) \times 1.10
   \]

   Simplify this expression:

   \[
   P_{2002} = P_{2000} \times 1.09 \times 1.10
   \]

   \[
   P_{2002} = P_{2000} \times 1.199
   \]

2. **Use the given population in 2002 to find \( P_{2000} \):**

   Given that \( P_{2002} = 24,930 \), we can set up the equation:

   \[
   24,930 = P_{2000} \times 1.199
   \]

   Solving for \( P_{2000} \):

   \[
   P_{2000} = \frac{24,930}{1.199}
   \]

3. **Calculate \( P_{2000} \):**

   \[
   P_{2000} \approx \frac{24,930}{1.199} \approx 20,788.16
   \]

Since population numbers are whole numbers, we round to the nearest integer:

\[
P_{2000} \approx 20,788
\]

### Conclusion:

The population of the town in the year 2000 was approximately **20,788**.

Would you like more details or have any questions?

### Related Questions:
1. What would the population be in 2003 if it increased by another 5% from 2002?
2. How would the calculation change if the population in 2001 was 8% more than in 2000 instead of 9%?
3. What would the population in 2000 be if the population in 2002 was instead 24,000?
4. If the population in 2002 was 10% less than in 2001, what would the population in 2000 be?
5. How would we calculate the population in a future year if the yearly increase rate changes each year?

**Tip:** When working with percentage increases, always convert percentages to decimals (e.g., 9% to 0.09) to simplify calculations.

Learn how to calculate the population of a town in the year 2000 based on given percentage increases in subsequent years. This problem involves using percentage increase formulas and basic algebraic calculations. Suitable for Grades 7-9 students.

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