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

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

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

Answer 1

To determine the worth of the copy machine in 10 years, we can first establish its rate of depreciation. The depreciation from year 0 to year 5 is as follows:

- Initially (year 0): Worth $10,500
- After 5 years: Worth $5,500

The decrease in value over 5 years is:

\[
10,500 - 5,500 = 5,000
\]

This means the copy machine loses $5,000 in value over 5 years.

To find the annual depreciation, we can divide the total depreciation by the number of years:

\[
\text{Annual Depreciation} = \frac{5,000}{5} = 1,000
\]

So, each year the copy machine loses $1,000 of its value.

Now, we can calculate its worth after 10 years:

After 5 years, the worth is $5,500. In the next 5 years, it will lose another $5,000 (5 years × $1,000/year):

\[
5,500 - 5,000 = 500
\]

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

So the correct response is:

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