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\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
& 1996 & 2006 & 2016 & Change (1996-2006) & Change (2006-2016) & Average Annual Rate (1996-2006) & Average Annual Rate (2006-2016) \\
\hline Transportation and utilities & [tex]$3,935.5$[/tex] & [tex]$4,405.8$[/tex] & [tex]$4,902.0$[/tex] & [tex]$530.3$[/tex] & [tex]$496.2$[/tex] & 1.3 & 1.1 \\
\hline Information & [tex]$2,940.0$[/tex] & [tex]$3,054.9$[/tex] & [tex]$3,266.7$[/tex] & [tex]$114.9$[/tex] & [tex]$211.8$[/tex] & 0.4 & 0.7 \\
\hline Financial activities & [tex]$6,968.6$[/tex] & [tex]$8,363.2$[/tex] & [tex]$9,570.1$[/tex] & [tex]$1,394.6$[/tex] & [tex]$1,206.9$[/tex] & 1.8 & 1.4 \\
\hline Professional and business services & [tex]$13,461.8$[/tex] & [tex]$17,551.6$[/tex] & [tex]$21,643.7$[/tex] & [tex]$4,089.8$[/tex] & [tex]$4,092.1$[/tex] & 2.7 & 2.1 \\
\hline Educational services & [tex]$2,077.5$[/tex] & [tex]$2,918.4$[/tex] & [tex]$3,527.4$[/tex] & [tex]$840.9$[/tex] & [tex]$609.0$[/tex] & 3.5 & 1.9 \\
\hline Health care and social assistance & [tex]$11,604.8$[/tex] & [tex]$14,919.8$[/tex] & [tex]$18,954.1$[/tex] & [tex]$3,315.0$[/tex] & [tex]$4,034.3$[/tex] & 2.5 & 2.4 \\
\hline Leisure and hospitality & [tex]$10,776.5$[/tex] & [tex]$13,143.4$[/tex] & [tex]$15,016.7$[/tex] & [tex]$2,366.9$[/tex] & [tex]$1,873.3$[/tex] & 2.0 & 1.3 \\
\hline Other services & [tex]$5,434.9$[/tex] & [tex]$6,234.6$[/tex] & [tex]$7,077.2$[/tex] & [tex]$799.7$[/tex] & [tex]$842.6$[/tex] & 1.4 & 1.3 \\
\hline Federal government & [tex]$2,877.0$[/tex] & [tex]$2,728.3$[/tex] & [tex]$2,625.7$[/tex] & -[tex]$148.7$[/tex] & -[tex]$102.6$[/tex] & -0.5 & -0.4 \\
\hline State and local government & [tex]$16,662.1$[/tex] & [tex]$19,261.7$[/tex] & [tex]$20,696.1$[/tex] & [tex]$2,599.6$[/tex] & [tex]$1,434.4$[/tex] & 1.5 & 0.7 \\
\hline
\end{tabular}

Based on the above chart, which industry's average annual rate of change is projected to decrease the most in the 2006-2016 period as compared to its average annual rate of change during 1996-2006?

a. Utilities
b. Educational services
c. Federal government
d. State and local government



Answer :

GinnyAnswer
To determine which industry's average annual rate of change is projected to decrease the most from the 1996-2006 period to the 2006-2016 period, follow these steps:

1. Identify the average annual rates of change for each industry during the 1996-2006 period and the 2006-2016 period from the table.

2. Calculate the decrease in the average annual rate of change for each industry by subtracting the average annual rate of change for the 2006-2016 period from the average annual rate of change for the 1996-2006 period.

3. Compare these decreases and identify the maximum decrease.

Here's the data from the table relevant to the problem:

- Educational services:
- Average annual rate of change (1996-2006): 3.5%
- Average annual rate of change (2006-2016): 1.9%
- Decrease: [tex]\(3.5\% - 1.9\% = 1.6\%\)[/tex]

- Federal government:
- Average annual rate of change (1996-2006): -0.5%
- Average annual rate of change (2006-2016): -0.4%
- Decrease: [tex]\(-0.5\% - (-0.4\%) = -0.1\%\)[/tex]

- State and local government:
- Average annual rate of change (1996-2006): 1.5%
- Average annual rate of change (2006-2016): 0.7%
- Decrease: [tex]\(1.5\% - 0.7\% = 0.8\%\)[/tex]

Based on the calculations above, the decreases are:

- Educational services: [tex]\(1.6\%\)[/tex]
- Federal government: [tex]\(-0.1\% \rightarrow 0.1\%\)[/tex] (decrease is smaller compared to others)
- State and local government: [tex]\(0.8\%\)[/tex]

Among these, the greatest decrease in the average annual rate of change is for Educational services with a decrease of [tex]\(1.6\%\)[/tex].

Thus, the industry whose average annual rate of change is projected to decrease the most in the 2006-2016 period, compared to the 1996-2006 period, is:

c. Federal government

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