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 order pair (5, 5,500). What will the machine be worth in 10 years?

1 answer

To determine the worth of the copy machine in 10 years, we can first find the depreciation rate by looking at its value over the first 5 years.

We know:

  • Initial value at year 0 (V0): $10,500
  • Value after 5 years (V5): $5,500

To find the annual depreciation, we can use the formula for depreciation:

\[ \text{Depreciation per year} = \frac{\text{Initial value} - \text{Value after 5 years}}{\text{Number of years}} \]

Substituting the values in:

\[ \text{Depreciation per year} = \frac{10,500 - 5,500}{5} = \frac{5,000}{5} = 1,000 \]

The copy machine depreciates by $1,000 each year.

Now, we can calculate the value of the machine in 10 years:

\[ \text{Value at year 10} = \text{Initial value} - (\text{Depreciation per year} \times \text{Number of years}) \]

Substituting the data:

\[ \text{Value at year 10} = 10,500 - (1,000 \times 10) = 10,500 - 10,000 = 500 \]

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