The gross federal debt y (in trillions of dollars) for a certain country in year x is approximated by the following equation, where x is the number of vears after 2000 y = 1.09x + 1.22 Assuming the trend continues, in what year will the federal debt be $26.29 trillion?

To find the year when the federal debt will be $26.29 trillion, we can use the given equation:

\[
y = 1.09x + 1.22
\]

where $ y $ is the gross federal debt (in trillions), and $ x $ is the number of years after 2000. We are given that $ y = 26.29 $. Substituting this into the equation:

\[
26.29 = 1.09x + 1.22
\]

Now, solve for $ x $:

1. Subtract 1.22 from both sides:

\[
26.29 - 1.22 = 1.09x
\]
\[
25.07 = 1.09x
\]

2. Divide both sides by 1.09 to isolate $ x $:

\[
x = \frac{25.07}{1.09} \approx 23
\]

Thus, $ x \approx 23 $, which means the year is $ 2000 + 23 = 2023 $.

So, the federal debt will be approximately $26.29 trillion in the year **2023**.

Would you like further details or have any questions? Here are some related questions you might find interesting:

1. What would the debt be in the year 2030, according to this model?
2. How does the rate of increase in debt compare with previous years?
3. How would a change in the annual growth rate affect the predicted debt?
4. What assumptions are made by this model, and how realistic are they?
5. What are the potential factors that could cause deviations from this trend?

**Tip:** Always check the underlying assumptions of financial models to ensure they match real-world conditions.

The gross federal debt y (in trillions of dollars) for a certain country in year x is approximated by the following equation, where x is the number of years after 2000 y = 1.09x + 1.22. Assuming the trend continues, in what year will the federal debt be $26.29 trillion?

Learn how to solve for the year when the federal debt will reach $26.29 trillion using the linear equation y = 1.09x + 1.22, where x represents years after 2000. This problem demonstrates key algebraic concepts, such as solving linear equations, and is suitable for students in Grades 9-12.

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