Question

A new truck costs $32,000. The car’s value will depreciate over time, which means it will lose value. For tax purposes, depreciation is usually calculated linearly. If the truck is worth $24,500 after three years, write an explicit formula for the value of the car after n years.

Answer 1

32000 - (32000 * .2552n)

Answer 2

v = -2500*n + 32000

Explanation:

Depreciation is usually calculated linearly, means that it follows the following equation (equation of a line):

v = a*n + b

where n is time after truck was new (in years), v is value of the truck (in $), and a and b are some constants.

A new truck costs $32,000, that is, when n = 0, v = 32000. Replacing into the equation:

32000 = a*0 + b

32000 = b

The truck is worth $24,500 after three years , that is, n = 3, v = 24500. Replacing into the equation:

24500 = a*3 + 32000

a*3 = 24500 - 32000

a = -7500/3 = -2500