Advanced MathVery hardFirst time decay falls below half
Advanced Math practice question
A machine's value is 20,000 dollars and falls 20 percent each year, so its value after t years is 20,000(0.8)ᵗ. What is the smallest whole number of years after which the value is below 10,000 dollars?
Answer: 4
0.8³ = 0.512 keeps the value at 10,240; 0.8⁴ = 0.4096 drops it to 8,192 — below half at t = 4.
Common wrong answers
- If you answered 2
- After 2 years the value is 12,800 dollars.
- If you answered 3
- After 3 years the value is 10,240 dollars, still above 10,000.
- If you answered 5
- Year 4 already drops the value to 8,192 dollars.
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