Question 30·Hard·Percentages
The stacked bar chart shows the total electricity generated in a country in 2010 and 2020, along with the amount generated from renewable sources.
If is the percent of the net increase in total electricity from 2010 to 2020 that is accounted for by the increase in renewable electricity, what is the value of ?
For “percent of a change accounted for by a component,” first compute both changes (component change and net total change). Then divide component change by net total change and multiply by 100. Be alert that the result can exceed 100% when other components decrease.
Hints
Compute changes, not totals
Find how much total electricity changed (), and how much renewable electricity changed ().
Use the net increase in total as the denominator
“Percent of the net increase accounted for by renewables” means
A percent can exceed 100% here
If nonrenewable electricity decreases while renewable electricity increases, the renewable increase can be larger than the net increase in total electricity.
Desmos Guide
Enter the net changes
In Desmos, enter:
180-160(net total increase)90-40(renewable increase)
Compute the percent
Enter:
100*(90-40)/(180-160)
The value shown is .
Step-by-step Explanation
Read the renewable and total amounts for each year
From the chart:
- 2010 total: TWh; 2010 renewable: TWh
- 2020 total: TWh; 2020 renewable: TWh
Compute the net change in total and the change in renewables
Net increase in total electricity:
Increase in renewable electricity:
Find the percent of the net increase accounted for by renewables
Compute renewables’ increase as a fraction of the net total increase:
Finish the calculation
So, the value of is .