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.
