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The problem states that Ana observed 324 black bears in a particular area and expects the population to increase by approximately 10% per year. We're asked to determine which equation represents the population of black bears, \( b \), after \( y \) years.

This scenario describes exponential growth, where the population increases by a fixed percentage each year. The formula for exponential growth is:

\[
b = P(1 + r)^y
\]

Where:
- \( P \) is the initial population (324 bears),
- \( r \) is the growth rate (10%, which is 0.1),
- \( y \) is the number of years.

Substituting the known values into the equation:

\[
b = 324(1 + 0.1)^y = 324(1.1)^y
\]

Therefore, the correct equation is **D: \( b = 324(1.1)^y \)**.

Would you like further details on this solution or have any questions? 

Here are 5 related questions to think about:
1. How would the equation change if the growth rate were 5% instead of 10%?
2. What would the population be after 5 years using this formula?
3. How does exponential growth differ from linear growth?
4. What is the population after 1 year, using this equation?
5. How would a decrease in population by 10% per year be represented?

**Tip**: When dealing with percentages in exponential growth, always convert the percentage to a decimal (e.g., 10% becomes 0.1).

Ana completed a study and noticed that there are 324 black bears in a certain area. She expects this population to increase by approximately 10% per year for the next several years. Which equation represents the approximate number of black bears, b, in y years?

Explore how to model population growth using exponential equations. Ana's study on black bears shows a 10% growth rate, with the equation b = 324(1.1)^y representing population over time.

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