High School

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Select the correct locations in the table.

The table shows the federal government's budgeted revenue and expenditures from 2001 through 2010. Identify the years in which there was a budget deficit.

[tex]
\[
\begin{tabular}{|l|l|l|}
\hline
Year & Revenue & Expenditure \\
\hline
2001 & \$8 trillion & \$6 trillion \\
\hline
2002 & \$5 trillion & \$7 trillion \\
\hline
2003 & \$8 trillion & \$10 trillion \\
\hline
2004 & \$9 trillion & \$7 trillion \\
\hline
2005 & \$15 trillion & \$18 trillion \\
\hline
2006 & \$8 trillion & \$10 trillion \\
\hline
2007 & \$6 trillion & \$4 trillion \\
\hline
2008 & \$2 trillion & \$10 trillion \\
\hline
\end{tabular}
\]
[/tex]

Identify the years with a budget deficit, where expenditures exceed revenue.

Answer :

We are given the federal government’s budget data for several years, with revenue and expenditure values expressed in trillions. A budget deficit occurs when the expenditure exceeds the revenue. In other words, if we let [tex]$R$[/tex] be the revenue and [tex]$E$[/tex] be the expenditure for a certain year, a deficit exists if

[tex]$$
R - E < 0.
$$[/tex]

Let’s go through the years one by one:

1. For 2001, the values are:
[tex]$$
R = 8,\quad E = 6.
$$[/tex]
The difference is
[tex]$$
8 - 6 = 2,
$$[/tex]
which is positive. Therefore, there is no budget deficit in 2001.

2. For 2002:
[tex]$$
R = 5,\quad E = 7.
$$[/tex]
The difference is
[tex]$$
5 - 7 = -2.
$$[/tex]
Since the result is negative, there is a budget deficit in 2002.

3. For 2003:
[tex]$$
R = 8,\quad E = 10.
$$[/tex]
The difference is
[tex]$$
8 - 10 = -2.
$$[/tex]
Again, the negative result indicates a budget deficit in 2003.

4. For 2004:
[tex]$$
R = 9,\quad E = 7.
$$[/tex]
The difference is
[tex]$$
9 - 7 = 2.
$$[/tex]
This is a surplus, so no deficit in 2004.

5. For 2005:
[tex]$$
R = 15,\quad E = 18.
$$[/tex]
The difference is
[tex]$$
15 - 18 = -3.
$$[/tex]
This negative amount shows a budget deficit in 2005.

6. For 2006:
[tex]$$
R = 8,\quad E = 10.
$$[/tex]
The difference is
[tex]$$
8 - 10 = -2.
$$[/tex]
The negative result indicates a budget deficit in 2006.

7. For 2007:
[tex]$$
R = 6,\quad E = 4.
$$[/tex]
The difference is
[tex]$$
6 - 4 = 2.
$$[/tex]
The positive result indicates that there is no deficit in 2007.

Thus, the years when the federal government ran a budget deficit are:

[tex]$$
2002,\ 2003,\ 2005,\ 2006.
$$[/tex]

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Rewritten by : Jeany