https://file.aiquickdraw.com/mathbot/file/17268413438907800pe2g.jpg

To solve the problem in the image, we need to compute:

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

From the table:
- \( f(5) = 7948.3 \) (US debt in year 5)
- \( f(1) = 5807.5 \) (US debt in year 1)

Now calculate the difference:

\[
f(5) - f(1) = 7948.3 - 5807.5 = 2140.8
\]

Now divide by 4 (since \(5 - 1 = 4\)):

\[
\frac{f(5) - f(1)}{5 - 1} = \frac{2140.8}{4} = 535.2
\]

Thus, the rate of increase in US debt is \( 535.2 \) billion dollars per year.

Now, what this tells us is that between years 1 and 5 (which correspond to the years 2001 and 2005), the US debt increased by an average of 535.2 billion dollars per year.

Would you like further details or have any other questions?

Here are 5 questions to consider:
1. What does this rate represent in terms of the economic conditions during the time?
2. How might this average rate of increase affect economic policies?
3. How does the increase from year 1 to year 5 compare to other periods in the table?
4. What external factors might contribute to such a debt increase?
5. How could such trends in debt affect future governmental planning?

**Tip:** When calculating average rates of change, always verify the units (years, billions, etc.) to ensure proper interpretation.

The following table gives values of D = f(t) (the total US debt in billions) t years after 2000. Evaluate (f(5) - f(1)) / (5 - 1) and say what it tells you about the US debt. Round the answer to one decimal place.

Calculate the average rate of increase in US debt between year 1 and year 5 after 2000 using the formula (f(5) - f(1)) / (5 - 1). The solution shows a step-by-step process resulting in a debt increase rate of 535.2 billion dollars per year.

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