A factory owner buys a new machine for $25,000. After eight years, the machine has a salvage value of $1,000. Find a formula for the value of the machine after t years, where $0 \leq t \leq 8$
A) V (t) = - 3,000x + 25,000
B) V (t) = - 3,000x + 1,000
C) V (t) = 3,000x + 25,000
D) V (t) = 3,000x - 25,000
E) V (t) = - 3,000x - 25,000

Question

Quizplus · Accepted Answer

The value of the machine decreases linearly from $25,000 to $1,000 over 8 years, which is a decrease of $24,000. Dividing this total decrease by the number of years gives a depreciation rate of $3,000 per year. Therefore, the formula for the value V(t) after t years is V(t) = 25,000 - 3,000t, which matches the form of choice A, albeit with a minor typographical error in the variable notation (x should be t).

A Factory Owner Buys a New Machine for $25,000 0≤t≤80 \leq t \leq 80≤t≤8

A Factory Owner Buys a New Machine for $25,000 $0 \leq t \leq 8$