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

Answer:

$V(n) =140000-10000n$

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

Step-by-step 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:

$m =\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{41000-140000}{9-0} = -10000$

Depreciation value = 10000

The value of truck is given by:

$V = \text{Initial cost}-\text{Depretiation value}\times \text{Age of truck}$

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