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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 as compared to its average annual rate of change during 1996-2006?

\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
Industry & 1996 & 2006 & 2016 & Change 1996-2006 & Change 2006-2016 & Annual Rate 1996-2006 & Annual Rate 2006-2016 \\
\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] & 799.7 & 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
Let's analyze the data to determine which industry experienced the greatest decrease in the average annual rate of change when comparing the periods 1996-2006 and 2006-2016.

The steps to find the industry with the maximum decrease are as follows:

1. Determine the average annual rate of change for each industry for both periods (1996-2006 and 2006-2016).
2. Calculate the difference in the average annual rate of change for each industry by subtracting the rate for 1996-2006 from the rate for 2006-2016.
3. Identify the industry with the maximum decrease.

Given the data, let's consider the average annual rates of change:
- For Utilities, the difference is [tex]\(-0.6 - (-1.5) = 0.9\)[/tex]
- For Wholesale trade, the difference is [tex]\(0.7 - 0.7 = 0\)[/tex]
- For Retail trade, the difference is [tex]\(0.4 - 0.8 = -0.4\)[/tex]
- For Transportation and warehousing, the difference is [tex]\(1.1 - 1.3 = -0.2\)[/tex]
- For Information, the difference is [tex]\(0.7 - 0.4 = 0.3\)[/tex]
- For Financial activities, the difference is [tex]\(1.4 - 1.8 = -0.4\)[/tex]
- For Professional and business services, the difference is [tex]\(2.1 - 2.7 = -0.6\)[/tex]
- For Educational services, the difference is [tex]\(1.9 - 3.5 = -1.6\)[/tex]
- For Health care and social assistance, the difference is [tex]\(2.4 - 2.5 = -0.1\)[/tex]
- For Leisure and hospitality, the difference is [tex]\(1.3 - 2.0 = -0.7\)[/tex]
- For Other services, the difference is [tex]\(1.3 - 1.4 = -0.1\)[/tex]
- For Federal government, the difference is [tex]\(-0.4 - (-0.5) = 0.1\)[/tex]
- For State and local government, the difference is [tex]\(0.7 - 1.5 = -0.8\)[/tex]

We now locate the industry with the maximum decrease, which corresponds to the minimum value in the list of differences:
- [tex]\(0.9, 0, -0.4, -0.2, 0.3, -0.4, -0.6, -1.6, -0.1, -0.7, -0.1, 0.1, -0.8\)[/tex]

The minimum value is [tex]\(-1.6\)[/tex], which is achieved by "Educational services."

Thus, the industry projected to experience the greatest decrease in the average annual rate of change from 1996-2006 to 2006-2016 is Educational services.

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