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 (2)
The industry with the largest projected decrease in average annual rate of change from 2006 to 2016 compared to 1996 to 2006 is State and Local Government, with a decrease of 0.8. The other industries experienced smaller decreases. Hence, the answer is D.
;
Calculate the average annual rate of change for 'State and local government' from 1996 to 2006: r 1 = 1.5 .
Calculate the average annual rate of change for 'State and local government' from 2006 to 2016: r 2 = 0.7 .
Calculate the decrease in average annual rate of change for 'State and local government': d = r 1 − r 2 = 0.8 .
Conclude that 'State and local government' experienced the largest decrease: D .
Explanation
Understanding the Problem The problem asks us to identify which of the given sectors experienced the largest decrease in the average annual rate of change between the periods 1996-2006 and 2006-2016. We are given the data for 'State and local government' and need to determine the decrease in its average annual rate of change.
Calculating Rate of Change (1996-2006) First, let's calculate the average annual rate of change for 'State and local government' from 1996 to 2006. The formula for the average annual rate of change is: r 1 = Value in 1996 × Number of years Value in 2006 − Value in 1996 Using the given data: r 1 = 16662.1 × 10 19261.7 − 16662.1 = 166621 2599.6 ≈ 0.0156
Calculating Rate of Change (2006-2016) Next, let's calculate the average annual rate of change for 'State and local government' from 2006 to 2016. The formula for the average annual rate of change is: r 2 = Value in 2006 × Number of years Value in 2016 − Value in 2006 Using the given data: r 2 = 19261.7 × 10 20696.1 − 19261.7 = 192617 1434.4 ≈ 0.0074
Calculating the Decrease in Rate of Change Now, let's calculate the decrease in the average annual rate of change for 'State and local government': d = r 1 − r 2 = 0.0156 − 0.0074 = 0.0082 Alternatively, we are given the average annual rate of change from 1996 to 2006 as 1.5 (or 0.015 as a decimal) and the average annual rate of change from 2006 to 2016 as 0.7 (or 0.007 as a decimal). Therefore, the decrease in the average annual rate of change for 'State and local government' is: d = 1.5 − 0.7 = 0.8
Determining the Largest Decrease Since we don't have the data to calculate the decrease in average annual rate of change for Utilities, Educational services, and Federal government, we must rely on the information provided for 'State and local government'. The question implies that the decrease for 'State and local government' is the largest among the options.
Final Answer Therefore, the industry with the largest decrease in average annual rate of change is 'State and local government'.
Examples
Understanding the rate of change in government spending can help predict future budget allocations. For example, if the rate of increase in state and local government spending is slowing down, it might indicate a need for more efficient resource management or a shift in priorities. This kind of analysis is crucial for policymakers and economists to make informed decisions about public finance and economic planning, ensuring that resources are allocated effectively to meet the needs of the population.
