A school district purchases a high-volume printer, copier, and scanner for $27,000. After 10 years, the equipment will have to be replaced. Its value at that time is expected to be $2000. Write a linear equation giving the value V of the equipment during the 10 years it will be in use. (Let t be the number of years after purchase.)

Question

Carlos Gregory

Mathematics

14 August, 05:22

A school district purchases a high-volume printer, copier, and scanner for $27,000. After 10 years, the equipment will have to be replaced. Its value at that time is expected to be $2000. Write a linear equation giving the value V of the equipment during the 10 years it will be in use. (Let t be the number of years after purchase.)

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Taylor Daugherty · Answer 1

V = 27000 - 2500t

Step-by-step explanation:

Let the linear equation that represents the value of the equipment after t years,

V = a - bt

Since, the original value of the equipment is $27,000,

That is, if t = 0, V = 27,000

27,000 = a - b (0)

⇒ a = 27,000

If t = 10, V = 2,000

2000 = a - 10b

2000 = 27,000 - 10b

10b = 25000

⇒ b = 2,500

Hence, the linear function that shows the value of the equipment after t years,

V = 27000 - 2500t