Advanced MathHardFirst year a decaying value falls below half
Advanced Math practice question
A machine loses 20% of its value each year. After how many whole years is its value first less than half of its original value?
Answer: 4
After n years the value is 0.8ⁿ of the original. 0.8³ = 0.512 (still above half), and 0.8⁴ = 0.4096 (below half). So 4 years.
Common wrong answers
- If you answered 3
- After 3 years the value is 0.512 of the original, still above half.
- If you answered 5
- 5 is later than the first year below half.
- If you answered 2.5
- 2.5 assumes a linear loss of 20% of the original each year (50 ÷ 20); the loss is 20% of the current value.
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