Question

A company paid ​$140 comma 000140,000 for a new​ 18-wheeler. When it is 99 years old it will be worth ​$41 comma 00041,000. Using​ straight-line depreciation, the value of the truck in​ dollars, V, is a linear function of its age in​ years, n. Find the function and the value when the truck is 88 years old.

Answer 1

`V(n) =140000-10000n`

The cost of truck when the truck is 8 years old is $60,000

Explanation:

We are given the following in the question:

Cost of new truck = $140,000

Cost of truck when 9 years old = $41,000

The depreciation is given by the slope of line:

`m =(y_2-y_1)/(x_2-x_1)=(41000-140000)/(9-0) = -10000`

Depreciation value = 10000

The value of truck is given by:

`V = \text{Initial cost}-\text{Depretiation value}* \text{Age of truck}`

Putting values, we get:

`V (n)= 140000 - 10000(n)\\V(n) =140000-10000n`

Value of truck at 8 years old:

`V(n) =140000-10000n\\V(8) =140000-10000(8) = 60000`

Thus, the cost of truck when the truck is 8 years old is $60,000