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The question asks for an explicit equation to represent the population of a town, \( y \), that starts at 15,000 people and grows by 1.5% per year.

Since this is a growth problem, we can use the formula for exponential growth:

\[
y = y_0 (1 + r)^t
\]

Where:
- \( y_0 \) is the initial population (15,000 people),
- \( r \) is the growth rate (1.5%, or 0.015 as a decimal),
- \( t \) is the time in years,
- \( y \) is the population after \( t \) years.

Substituting the given values:

\[
y = 15,000 (1 + 0.015)^t
\]

Simplifying:

\[
y = 15,000 (1.015)^t
\]

This is the explicit equation for the population growth of the town.

Would you like further explanation, or do you have any questions?

Here are 5 related questions to further your understanding:

1. How would the equation change if the growth rate was 2% instead of 1.5%?
2. How would you calculate the population after 5 years using this equation?
3. What happens to the population if the growth rate is negative (i.e., a population decline)?
4. Can you express the growth rate as a fraction instead of a decimal? How would that affect the equation?
5. How would the equation change if the population was growing by a fixed amount (e.g., 500 people per year) instead of a percentage?

**Tip:** When dealing with growth or decay problems, always pay attention to whether the growth is given as a percentage (exponential growth) or a fixed amount (linear growth).

The population of a town, y, is 15,000 people and is growing by 1.5% per year.

Learn how to derive the explicit equation for a town's population starting at 15,000 and growing by 1.5% annually. This solution involves the exponential growth formula y = y0(1 + r)^t and is suitable for students in Grades 9-11.

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