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1. **Problem Overview**: The population of a town grew from 11,500 in 1990 to 17,100 in 1997. You need to:
    - Fill in a table with the number of years after 1990 and the population.
    - Calculate how many years passed.
    - Determine the population change.
    - Calculate the average rate of growth per year.

### a. Completing the table of values
- **1990**: Let the time since 1990 be \( t \). In 1990, \( t = 0 \) and the population \( P = 11,500 \).
- **1997**: Since 1997 is 7 years after 1990, \( t = 7 \), and the population \( P = 17,100 \).

### b. Population change \( \Delta P \)
The population change is given by:
\[
\Delta P = P_{1997} - P_{1990} = 17,100 - 11,500 = 5,600
\]

### c. How many years passed \( \Delta t \)
The time difference between 1990 and 1997 is:
\[
\Delta t = 1997 - 1990 = 7 \text{ years}
\]

### d. Average rate of growth \( \frac{\Delta P}{\Delta t} \)
The average rate of growth is:
\[
\text{Average rate of growth} = \frac{\Delta P}{\Delta t} = \frac{5,600}{7} = 800 \text{ people per year}
\]

### e. Average annual growth
The average annual growth is the same as the rate of growth found in part d:
\[
\text{Average annual growth} = 800 \text{ people per year}
\]

### Summary:
- **1990**: \( t = 0 \), \( P = 11,500 \)
- **1997**: \( t = 7 \), \( P = 17,100 \)
- **Population change \( \Delta P \)**: 5,600 people
- **Years passed \( \Delta t \)**: 7 years
- **Average rate of growth**: 800 people per year

Would you like more details on any of these steps? Here are 5 related questions you can explore:
1. How would the population change if the rate of growth doubled?
2. What if the population in 1997 was only 15,000? How would the growth rate change?
3. Can you model this population growth using a linear equation?
4. What would the population be in 2025 at the same growth rate?
5. How does this growth rate compare to exponential growth?

**Tip**: When dealing with growth problems, always remember that rate is calculated as the change in quantity divided by the time elapsed.

The population of a town grew from 11,500 in 1990 to 17,100 in 1997. Fill in the table, calculate population change, time passed, and average rate of growth.

Learn how to calculate the population growth of a town between 1990 and 1997, where the population increased from 11,500 to 17,100. This problem involves calculating time passed, population change, and the average rate of growth.

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