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The question asks to evaluate the average rate of change of the U.S. debt from year 1 to year 5 using the formula:

\[
\frac{f(5) - f(1)}{5 - 1}
\]

Where:

- \( f(5) \) is the U.S. debt at year 5, and
- \( f(1) \) is the U.S. debt at year 1.

From the table:

- \( f(5) = 7993.6 \) (U.S. debt at year 5),
- \( f(1) = 5813.8 \) (U.S. debt at year 1).

Now, let's calculate the average rate of change:

\[
\frac{7993.6 - 5813.8}{5 - 1} = \frac{2179.8}{4}
\]

I will now compute this.The average rate of change of the U.S. debt from year 1 to year 5 is approximately **544.95 billion dollars per year**.

This value tells us that, on average, the U.S. debt increased by around **544.95 billion dollars** per year during this time period.

Do you have any questions or need more details?

Here are 5 related questions to explore further:
1. What does the average rate of change represent in real-world terms?
2. How would the average rate of change differ if we chose years 3 and 7 instead?
3. Can we predict future debt values using this rate of change?
4. How does this average rate compare to other time intervals in the table?
5. How would rounding affect the interpretation of the rate?

**Tip:** The average rate of change between two points is equivalent to the slope of the line connecting them on a graph.

The following table gives values of D = f(t), the total US debt (in billions of dollars) t years after 2000. Evaluate (f(5) - f(1)) / (5 - 1) and explain what it tells you about the US debt.

Learn how to calculate the average rate of change of the US debt between years 1 and 5 using a step-by-step approach. This example demonstrates how to interpret the slope formula in real-world applications and covers important concepts like linear approximation. Suitable for high school students in Grades 10-12.

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