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The problem states that there were 10,000 students in a school district in 2010, and the number of students is expected to decrease by 0.8% per year. We are asked to write an exponential model for this situation and find the number of students in 2020.

### Step 1: Create the exponential model
The general form of an exponential decay model is:

\[
N(t) = N_0 \cdot (1 - r)^t
\]

Where:
- \( N(t) \) is the number of students at time \( t \).
- \( N_0 \) is the initial number of students.
- \( r \) is the annual decay rate (in decimal form).
- \( t \) is the number of years since the initial time.

### Step 2: Assign values from the problem
- \( N_0 = 10,000 \) (the number of students in 2010).
- \( r = 0.008 \) (the 0.8% decrease per year).
- The number of years from 2010 to 2020 is \( t = 10 \).

### Step 3: Write the exponential model
The exponential model for this situation is:

\[
N(t) = 10,000 \cdot (1 - 0.008)^t
\]

Simplifying the decay factor:

\[
N(t) = 10,000 \cdot (0.992)^t
\]

### Step 4: Calculate the number of students in 2020
Substitute \( t = 10 \) into the model to find the number of students in 2020:

\[
N(10) = 10,000 \cdot (0.992)^{10}
\]

Let me calculate that.The number of students in the school district in 2020, based on the exponential model, is approximately 9,228.

Would you like more details or have any questions about this calculation? 

Here are 5 related questions for further exploration:
1. How would the model change if the rate of decrease was 1.5% instead of 0.8%?
2. What would happen to the population if the decay rate was compounded quarterly instead of annually?
3. How many students would be left after 20 years, following the same model?
4. How can we use this model to predict the year in which the population will drop below 5,000?
5. How does this type of exponential decay compare to a linear decrease?

**Tip:** In exponential decay problems, the decrease rate has a compounding effect, meaning the total reduction grows larger over time.

There were 10,000 students in a school district in 2010. The number of students is expected to decrease by 0.8% each year. Write an exponential model and find the number of students in 2020.

Learn how to solve an exponential decay problem where a school district starts with 10,000 students in 2010, decreasing by 0.8% annually. Find the number of students in 2020 using the exponential decay formula. Suitable for Grades 9-12.

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