AlgebraMediumFirst year a linearly depreciating value falls below a threshold
Algebra practice question
The value of a machine t years after purchase is V(t) = 18,000 − 1,500t dollars. After how many whole years will the value first be less than $6,000?
Answer: 9
18,000 − 1,500t < 6,000 → 1,500t > 12,000 → t > 8. The first whole year is 9.
Common wrong answers
- If you answered 4
- 4 comes from 6,000 ÷ 1,500.
- If you answered 8
- After 8 years the value is exactly $6,000, not less than it.
- If you answered 12
- 12 is when the value reaches $0.
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