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The problem states that a restaurant chain currently owns 2000 restaurants and predicts a growth of 3% per year. We are tasked with identifying the equation that represents the number of restaurants \( y \) as a function of time \( t \), in years.

This is an exponential growth scenario, where the number of restaurants increases by a constant percentage each year. The general form of an exponential growth model is:

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

Where:
- \( y_0 \) is the initial amount (2000 restaurants),
- \( r \) is the growth rate (3% = 0.03),
- \( t \) is the number of years.

Substituting the values, the equation becomes:

\[
y = 2000(1.03)^t
\]

This corresponds to option **D**: \( y = 2000(1.03)^t \).

Would you like more details or explanations?

Here are 5 related questions to expand your understanding:
1. How does the value of \( r \) (growth rate) affect the speed of growth in an exponential function?
2. What happens to the number of restaurants if the growth rate decreases to 2%?
3. How would the equation change if the initial number of restaurants was 3000?
4. What is the difference between exponential growth and linear growth?
5. How can you calculate the time it takes to double the number of restaurants at a 3% growth rate?

**Tip:** In exponential growth models, small changes in the growth rate can significantly impact long-term outcomes due to compounding effects.

A restaurant chain currently owns 2000 restaurants. The chain's business model predicts that the number of restaurants will grow by approximately 3% each year. Which equation represents the number of restaurants (y) the business model predicts the chain will own over time (t), in years?

Learn how to represent the growth of a restaurant chain using an exponential growth equation. The problem involves predicting the number of restaurants over time with a 3% annual growth, modeled by the equation y = 2000(1.03)^t. Suitable for high school students in Grades 9-12.

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