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\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
& 1996 & 2006 & 2016 & Change (1996-2006) & Change (2006-2016) & Avg. Annual Rate (1996-2006) & Avg. Annual Rate (2006-2016) \\
\hline
Financial activities & [tex]$2,940.0$[/tex] & [tex]$3,054.9$[/tex] & [tex]$3,266.7$[/tex] & 114.9 & 211.8 & 0.4 & 0.7 \\
\hline
Professional and business services & [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
Educational 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
Health care and social assistance & [tex]$2,077.5$[/tex] & [tex]$2,918.4$[/tex] & [tex]$3,527.4$[/tex] & 840.9 & 609.0 & 3.5 & 1.9 \\
\hline
Leisure and hospitality & [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
Other services & [tex]$10,776.5$[/tex] & [tex]$13,143.4$[/tex] & [tex]$15,016.7$[/tex] & 2,366.9 & [tex]$1,873.3$[/tex] & 2.0 & 1.3 \\
\hline
Federal government & [tex]$5,434.9$[/tex] & [tex]$6,234.6$[/tex] & [tex]$7,077.2$[/tex] & 799.7 & 842.6 & 1.4 & 1.3 \\
\hline
State and local government & [tex]$2,877.0$[/tex] & [tex]$2,728.3$[/tex] & [tex]$2,625.7$[/tex] & -148.7 & -102.6 & -0.5 & -0.4 \\
\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 between the 2006-2016 period compared to the 1996-2006 period, we should calculate the difference in the average annual rates of change for each industry between the two periods.

Given the rates for each period:
- Financial activities: 0.4 (1996-2006) and 0.7 (2006-2016)
- Professional and business services: 1.8 (1996-2006) and 1.4 (2006-2016)
- Educational services: 2.7 (1996-2006) and 2.1 (2006-2016)
- Health care and social assistance: 3.5 (1996-2006) and 1.9 (2006-2016)
- Leisure and hospitality: 2.5 (1996-2006) and 2.4 (2006-2016)
- Other services: 2.0 (1996-2006) and 1.3 (2006-2016)
- Federal government: 1.4 (1996-2006) and 1.3 (2006-2016)
- State and local government: -0.5 (1996-2006) and -0.4 (2006-2016)

We will find the difference in the rates for each industry:

1. Financial activities:
[tex]\[ 0.7 - 0.4 = 0.3 \text{ (increase)} \][/tex]
2. Professional and business services:
[tex]\[ 1.4 - 1.8 = -0.4 \text{ (decrease)} \][/tex]
3. Educational services:
[tex]\[ 2.1 - 2.7 = -0.6 \text{ (decrease)} \][/tex]
4. Health care and social assistance:
[tex]\[ 1.9 - 3.5 = -1.6 \text{ (decrease)} \][/tex]
5. Leisure and hospitality:
[tex]\[ 2.4 - 2.5 = -0.1 \text{ (decrease)} \][/tex]
6. Other services:
[tex]\[ 1.3 - 2.0 = -0.7 \text{ (decrease)} \][/tex]
7. Federal government:
[tex]\[ 1.3 - 1.4 = -0.1 \text{ (decrease)} \][/tex]
8. State and local government:
[tex]\[ -0.4 - (-0.5) = -0.4 + 0.5 = 0.1 \text{ (increase)} \][/tex]

Now, we determine the industry with the maximum decrease. From the above calculations, the highest decrease in the average annual rate of change is:

- Health care and social assistance: -1.6

Therefore, based on the given data, 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 Health care and social assistance. However, the given options do not list this industry. As such, we should recheck and choose from the given options:

Among the options provided (a. Utilities, b. Educational services, c. Federal government, d. State and local government), we see:

b. Educational services has a decrease of -0.6, which is the highest decrease among these options.

So, the correct answer among the given options is:
b. Educational services

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