A company buys a copy machine for $10,500 and is represented by the ordered pair (0,10,500)

. After 5 years, it is worth $5,500 and is represented by the ordered pair (5,5,500)
. What will the machine be worth in 10 years?(1 point)
Responses

After 10 years, the copy machine is worth $10,500.
After 10 years, the copy machine is worth $10,500.

After 500 years, the copy machine is worth $10.
After 500 years, the copy machine is worth $10.

After 10 years, the copy machine is worth $500.
After 10 years, the copy machine is worth $500.

After 10 years, the copy machine is worth $9,500.

1 answer

To find the worth of the copy machine in 10 years, we can first determine the annual depreciation of the machine by looking at the change in value from year 0 to year 5.

The initial value (at year 0) is $10,500, and the value after 5 years is $5,500.

Here’s the calculation for depreciation over 5 years:

  1. Calculate the total depreciation over 5 years: \[ \text{Depreciation} = \text{Initial Value} - \text{Value after 5 years} = 10,500 - 5,500 = 5,000 \]

  2. Find the annual depreciation: \[ \text{Annual Depreciation} = \frac{\text{Total Depreciation}}{\text{Number of Years}} = \frac{5,000}{5} = 1,000 \]

  3. Project the value after 10 years:

    • After another 5 years (making it a total of 10 years), the machine will depreciate an additional \( 5 \times 1,000 = 5,000 \).
    • Therefore, the value after 10 years will be: \[ \text{Value after 10 years} = \text{Value after 5 years} - \text{Additional Depreciation} = 5,500 - 5,000 = 500 \]

Thus, the machine will be worth $500 after 10 years.

The correct response is: After 10 years, the copy machine is worth $500.