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

\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
& & & & & & & \\
\hline
Utilities & 639.5 & 548.5 & 517.6 & -91.0 & -30.9 & -1.5 & -0.6 \\
\hline
Wholesale trade & [tex]$5,522.1$[/tex] & [tex]$5,897.7$[/tex] & [tex]$6,326.2$[/tex] & 375.6 & 428.5 & 0.7 & 0.7 \\
\hline
Retail trade & [tex]$14,142.6$[/tex] & [tex]$15,319.4$[/tex] & [tex]$16,006.4$[/tex] & [tex]$1,176.8$[/tex] & 687.0 & 0.8 & 0.4 \\
\hline
Transportation and warehousing & [tex]$3,935.5$[/tex] & [tex]$4,465.8$[/tex] & [tex]$4,962.0$[/tex] & 530.3 & 496.2 & 1.3 & 1.1 \\
\hline
Information & [tex]$2,940.0$[/tex] & [tex]$3,054.9$[/tex] & [tex]$3,266.7$[/tex] & 114.9 & 211.8 & 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] & 840.9 & 609.0 & 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]$799.0$[/tex] & 842.6 & 1.4 & 1.3 \\
\hline
Federal 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
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}



Answer :

GinnyAnswer
To determine which industry's average annual rate of change is projected to decrease the most in the 2006-2016 period compared to its rate during the 1996-2006 period, let's analyze the differences in rates for each industry step by step.

For each industry, subtract the rate of the 1996-2006 period from the rate of the 2006-2016 period, then consider the absolute value of this difference to find the magnitude of the decrease:

1. Utilities:
[tex]\[ \left|-0.6 - (-1.5)\right| = \left|-0.6 + 1.5\right| = 0.9 \][/tex]

2. Wholesale trade:
[tex]\[ \left|0.7 - 0.7\right| = 0.0 \][/tex]

3. Retail trade:
[tex]\[ \left|0.4 - 0.8\right| = \left|-0.4\right| = 0.4 \][/tex]

4. Transportation and warehousing:
[tex]\[ \left|1.1 - 1.3\right| = \left|-0.2\right| = 0.2 \][/tex]

5. Information:
[tex]\[ \left|0.7 - 0.4\right| = \left|0.3\right| = 0.3 \][/tex]

6. Financial activities:
[tex]\[ \left|1.4 - 1.8\right| = \left|-0.4\right| = 0.4 \][/tex]

7. Professional and business services:
[tex]\[ \left|2.1 - 2.7\right| = \left|-0.6\right| = 0.6 \][/tex]

8. Educational services:
[tex]\[ \left|1.9 - 3.5\right| = \left|-1.6\right| = 1.6 \][/tex]

9. Health care and social assistance:
[tex]\[ \left|2.4 - 2.5\right| = \left|-0.1\right| = 0.1 \][/tex]

10. Leisure and hospitality:
[tex]\[ \left|1.3 - 2.0\right| = \left|-0.7\right| = 0.7 \][/tex]

11. Other services:
[tex]\[ \left|1.3 - 1.4\right| = \left|-0.1\right| = 0.1 \][/tex]

12. Federal government:
[tex]\[ \left|-0.4 - (-0.5)\right| = \left|-0.4 + 0.5\right| = 0.1 \][/tex]

13. State and local government:
[tex]\[ \left|0.7 - 1.5\right| = \left|-0.8\right| = 0.8 \][/tex]

Now, comparing all these absolute differences, the industry with the largest difference is Educational services, with a decrease of [tex]\(1.6\)[/tex].

Therefore, the industry's average annual rate of change that is projected to decrease the most in the 2006-2016 period compared to its rate during the 1996-2006 period is:

Educational services with a decrease of [tex]\(1.6\)[/tex].

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