Question

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

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

Answer 1

To determine the value of the copy machine after 10 years, we can look at the depreciation between the two values given:

1. **Initial Value:** $10,500 at Year 0 (represented by the ordered pair (0, 10,500))
2. **Value after 5 years:** $5,500 at Year 5 (represented by the ordered pair (5, 5,500))

Now, we’ll calculate the annual depreciation using the values provided:

- The depreciation over 5 years = Initial Value - Value after 5 years
- Depreciation = $10,500 - $5,500 = $5,000

Now, we can find the annual depreciation:

\[
\text{Annual Depreciation} = \frac{\text{Total Depreciation}}{\text{Number of Years}} = \frac{\$5,000}{5} = \$1,000
\]

Now, we can apply this annual depreciation for another 5 years (from Year 5 to Year 10):

- Value after another 5 years = Value after 5 years - (Annual Depreciation × Number of Years)
- Value after 10 years = $5,500 - ($1,000 × 5) = $5,500 - $5,000 = $500

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

**Final Response:** After 10 years, the copy machine is worth $500.