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A company purchased a machine valued at $\$ 120,000$. The value of the machine depreciates by the same amount each year so that after 10 years the value will be $\$ 30,000$. Which of the following equations gives the value, $v$, of the machine, in dollars, $t$ years after it was purchased for $0 \leq t \leq 10 ?$

SAT · Math · previous-year question

  1. A.$v=30,000-9,000 t$
  2. B.$v=120,000-9,000 t$correct
  3. C.$v=120,000+9,000 t$
  4. D.$v=120,000-30,000 t$

Answer

B. $v=120,000-9,000 t$

Explanation

Choice B is correct. The difference between the machine's starting value and its value after 10 years can be found by subtracting $\$ 30,000$ from $\$ 120,000: 120,000-30,000=90,000$. It's given that the value of the machine depreciates by the same amount each year for 10 years. Dividing $\$ 90,000$ by 10 gives $\$ 9,000$, which is the amount by which the value depreciates each year. Therefore, over a period of $t$ years, the value of the machine depreciates by a total of $9,000 t$ dollars. The value $v$ of the machine, in dollars, $t$ years after it was purchased is the starting value minus t

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