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Difficulty: EasyPercentages, Percent Change, and Interest

A residential solar power system generated 40004{}000 kilowatt-hours (kWh\text{kWh}) of electricity during its first year of operation. In the second year, electricity generation decreased by 10%10\%. In the third year, electricity generation increased by 10%10\% relative to the second year's generation. How many kilowatt-hours of electricity did the solar system generate in the third year?

  1. A
    32403{}240
  2. B
    36003{}600
  3. 39603{}960Answer
  4. D
    40004{}000
  5. E
    44004{}400

Answer

The solar power system generated 3960 kWh3{}960\text{ kWh} of electricity in the third year.
In the first year, generation was 4000 kWh4{}000\text{ kWh}. A 10%10\% decrease yields 4000×(1−0.10)=3600 kWh4{}000 \times (1 - 0.10) = 3{}600\text{ kWh} for the second year. In the third year, a 10%10\% increase over the second year's generation yields 3600×(1+0.10)=3960 kWh3{}600 \times (1 + 0.10) = 3{}960\text{ kWh}.

Step-by-Step Solution

1
Calculate the electricity generated in the second year after a 10%10\% decrease from the first year.
4000−(0.10×4000)=4000−400=3600 kWh4{}000 - (0.10 \times 4{}000) = 4{}000 - 400 = 3{}600\text{ kWh}
A 10%10\% decrease means retaining 90%90\% of the original 4000 kWh4{}000\text{ kWh} base.
2
Calculate the electricity generated in the third year after a 10%10\% increase over the second year's total.
3600+(0.10×3600)=3600+360=3960 kWh3{}600 + (0.10 \times 3{}600) = 3{}600 + 360 = 3{}960\text{ kWh}
The 10%10\% increase applies to the new base value of 3600 kWh3{}600\text{ kWh}, not the initial 4000 kWh4{}000\text{ kWh}.

Key Concept

Successive Percent Changes and Base Shifts
Estimated Time:45s
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Topics

Percentages, Percent Change, and Interest

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