AlgebraEasy–MediumInterpreting slope in a depreciation model
Algebra practice question
The value of a bottling machine is modeled by v(t) = 48,000 − 3,200t dollars, where t is years since purchase. What does 3,200 represent in this model?
- A. The amount the machine's value falls each yearCorrect
- B. The machine's value when it was purchased
- C. The number of years before the machine is worthless
- D. The machine's scrap value
Answer: A. The amount the machine's value falls each year
The coefficient of t is the rate of change: each added year removes 3,200 dollars from the value.
Why the other answers are wrong
- B. The machine's value when it was purchased
- The purchase value is the constant term, 48,000.
- C. The number of years before the machine is worthless
- The machine reaches value 0 at t = 48,000 ÷ 3,200 = 15 years — that is computed from both numbers, not 3,200 itself.
- D. The machine's scrap value
- The model gives no scrap value; 3,200 multiplies t, so it is a yearly rate.
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