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The problem is asking to evaluate the expression \(\frac{f(5) - f(1)}{5 - 1}\), where \(f(t)\) represents the total US debt \(D(t)\) in billions of dollars at year \(t\) after 2000. The table provides the values of \(D(t)\) for various years \(t\), with the relevant values being:

- \(f(5) = 7993.6\) (total debt at \(t = 5\))
- \(f(1) = 5813.8\) (total debt at \(t = 1\))

Now, let's calculate \(\frac{f(5) - f(1)}{5 - 1}\):

\[
\frac{f(5) - f(1)}{5 - 1} = \frac{7993.6 - 5813.8}{5 - 1} = \frac{2179.8}{4} = 544.95
\]

So the average increase in US debt between 2001 and 2005 is approximately **544.95 billion dollars per year**.

The input you've provided shows **44.95 billion dollars per year**, which is significantly lower, hence the partial correctness feedback.

Would you like more details on this calculation or any related concepts? Here are some follow-up questions:

1. How is the average rate of change between two points calculated in general?
2. Can this method be applied to any data set representing change over time?
3. Why might the debt increase rate change between different time periods?
4. How could this data be used to project future debt levels?
5. What could cause deviations in the calculated average increase?

**Tip:** Always double-check the calculation steps, especially when interpreting large numbers to ensure accuracy in real-world applications like financial data.

Evaluate \(\frac{f(5) - f(1)}{5 - 1}\) based on the US debt values given in a table, and interpret what it tells you about the US debt.

This problem involves calculating the average rate of change in US debt between 2001 and 2005. Using data provided in a table, the solution includes key concepts of linear functions and the Mean Value Theorem. Suitable for high school students in Grades 10-12.

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