The fox population in a certain region has an annual growth rate of 8% per year. In the year 2012, there were 24,800 foxes counted in the area. What is the fox population predicted to be in the year 2020?

To determine the predicted fox population in 2020, we can use the formula for exponential growth:

\[
P = P_0 \times (1 + r)^t
\]

where:
- \( P \) is the predicted population,
- \( P_0 \) is the initial population,
- \( r \) is the growth rate (as a decimal),
- \( t \) is the time in years from the initial count.

### Step-by-Step Solution

1. **Identify the values:**
   - Initial population (\( P_0 \)) = 24,800 foxes
   - Annual growth rate (\( r \)) = 8% = 0.08
   - Time period (\( t \)) from 2012 to 2020 = 2020 - 2012 = 8 years

2. **Plugging values into the formula:**

   \[
   P = 24,800 \times (1 + 0.08)^8
   \]

3. **Calculating the expression:**
   - First, calculate \( 1 + 0.08 = 1.08 \).
   - Raise \( 1.08 \) to the power of 8:
     \[
     1.08^8 \approx 1.85093
     \]
   - Now, multiply by the initial population:
     \[
     P \approx 24,800 \times 1.85093 \approx 45,924
     \]

### Answer:
The predicted fox population in 2020 is approximately **45,924 foxes**.

Would you like further details or have any questions?

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Here are five related questions to explore:

1. How would the population change if the growth rate was only 5% per year?
2. What would the population be in 2025 at the same growth rate?
3. How long would it take for the fox population to double at an 8% growth rate?
4. If the growth rate fluctuates yearly, how could we model the population growth?
5. How would the model change if the population had a yearly decrease instead?

**Tip:** In exponential growth, even small percentage changes can lead to significant differences over time.

The fox population in a certain region has an annual growth rate of 8% per year. In the year 2012, there were 24,800 foxes counted in the area. What is the fox population predicted to be in the year 2020?

Explore how to predict fox population growth with an annual growth rate of 8%. Given a population of 24,800 foxes in 2012, learn how to calculate the expected population in 2020 using exponential growth modeling. Ideal for high school math students covering exponential growth.

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