To determine 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, we need to compare the differences in the rates for each industry provided in the table.
Given:
- Utilities: Not given
- Educational Services: 3.5 (1996-2006), 1.9 (2006-2016)
- Federal Government: -0.5 (1996-2006), -0.4 (2006-2016)
- State and Local Government: 1.5 (1996-2006), 0.7 (2006-2016)
We calculate the difference for each industry between the two periods:
1. Educational services:
[tex]\[
\text{Difference} = 3.5 - 1.9 = 1.6
\][/tex]
2. Federal government:
[tex]\[
\text{Difference} = -0.5 - (-0.4) = -0.5 + 0.4 = -0.1
\][/tex]
3. State and local government:
[tex]\[
\text{Difference} = 1.5 - 0.7 = 0.8
\][/tex]
Next, we identify which difference is the greatest decrease:
- Educational services: 1.6
- Federal government: -0.1
- State and local government: 0.8
The industry that shows the greatest decrease (i.e., the largest positive difference indicating a reduction in growth rate) is Educational services, with a decrease of 1.6.
Therefore, the industry's average annual rate of change projected to decrease the most in the 2006-2016 period compared to its average annual rate during 1996-2006 is:
b. Educational services
