Question

Last week a theater purchases an air conditioner for $20,000. The air conditioner’s value will depreciate $2,000 a year for each of the next 10 years. The equation y = 20,000 – 2,000x, 0≤x≤10 models the air conditioner’s value, where y is the number of years after purchase. In how many years will the value of the air conditioner be $8,000?

Answer 1

To find out in how many years the value of the air conditioner will be $8,000, we set up the equation y = $20,000 - $2,000x, with y being $8,000, and solve for x. By simplification, we find that it will take 6 years for the air conditioner to depreciate to a value of $8,000.

Step-by-step explanation:

The student is asking when the value of an air conditioner will depreciate to $8,000 given the depreciation model y = 20,000 – 2,000x, where y is the value in dollars and x is the number of years after purchase, within a span of 10 years. To find the number of years it takes for the air conditioner's value to depreciate to $8,000, we can set y to $8,000 and solve for x in the given equation:

y = 20,000 – 2,000x

$8,000 = 20,000 – 2,000x

Subtract 20,000 from both sides to isolate the term with x:

–$12,000 = – 2,000x

Divide both sides by -2,000 to solve for x:

x = 6

Therefore, it will take 6 years for the air conditioner's value to depreciate to $8,000.