What is the average annual growth rate of CO2 emissions in power sector ?
2014
What is the average annual growth rate of CO2 emissions in power sector ?
Answer: A. ~12.57% — ConceptThe average annual growth rate of a quantity over several years is the arithmetic mean of its year-on-year percentage changes. For two consecutive…
- A.
~12.57%
- B.
~16.87%
- C.
~30.81%
- D.
~50.25%
Show answer & explanation
Correct answer: A
Concept
The average annual growth rate of a quantity over several years is the arithmetic mean of its year-on-year percentage changes. For two consecutive years, the growth rate of the later year is given by:
(Vnext − Vprev) ÷ Vprev × 100
The denominator is always the earlier year’s value, and a list of n + 1 data years contains exactly n one-year intervals. So the average annual growth rate = (sum of the n annual rates) ÷ n — divided by the number of intervals, not by the number of years listed.
Application
Read only the Power column of the table: 2005 = 500, 2006 = 600, 2007 = 650, 2008 = 700 and 2009 = 800 (million metric tons). Five data years give four consecutive one-year intervals.
Interval | Calculation | Annual growth rate |
|---|---|---|
2005 → 2006 | (600 − 500) ÷ 500 × 100 | 20.00% |
2006 → 2007 | (650 − 600) ÷ 600 × 100 | 8.33% |
2007 → 2008 | (700 − 650) ÷ 650 × 100 | 7.69% |
2008 → 2009 | (800 − 700) ÷ 700 × 100 | 14.29% |
Add the four annual rates: 20.00 + 8.33 + 7.69 + 14.29 = 50.31%.
Divide that total by the number of intervals, which is 4: 50.31 ÷ 4 = 12.58%.
To the precision offered by the choices, the average annual growth rate of the power sector is about 12.57%.
Cross-check
A compound (geometric) check agrees. The compound annual growth rate over the same span is:
(800 ÷ 500)1/4 − 1 = 1.60.25 − 1 ≈ 12.47%
That compound figure of about 12.47% per year sits right beside the arithmetic mean of 12.58% and confirms the scale of the result.
Two slips change the size of the answer sharply: leaving the total of 50.31% un-averaged, or dividing it by 3 instead of by the 4 actual one-year intervals. Both give figures far larger than the correct 12.57%.