the population, y, of the town of smith land in x years is modeled by the equation y=8000(1.02)x

The population model for Smith Land is given by the equation:

\[
y = 8000 \times (1.02)^x
\]

where:
- \( y \) represents the population of the town,
- \( 8000 \) is the initial population (at \( x = 0 \)),
- \( 1.02 \) is the growth factor, indicating a 2% increase per year,
- \( x \) represents the number of years from the initial measurement.

This is an example of exponential growth, where the population increases by 2% each year. 

Would you like more details, or do you have any questions?

### Related Questions:
1. What will the population be in 10 years?
2. How long will it take for the population to double?
3. What would the model look like with a 3% growth rate instead?
4. If the growth rate was only 1%, how would it affect the population over time?
5. How does exponential growth compare to linear growth?

#### Tip:
For exponential growth, the population grows by a constant percentage, not a constant amount, each year.

Explore the exponential growth model for the population of Smith Land, represented by the equation y = 8000(1.02)^x. This equation illustrates a 2% annual growth rate, starting from an initial population of 8000. Suitable for Grades 7-9.

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