Question

Solve the problem. The yearly depreciation rate for a certain vehicle is modeled by r = 1 - (*) Im where V is the value of the car after n years, and C is the original cost. a. Determine the depreciation rate for a car that originally cost $18,000 and is worth $11,000 after 3 yr. Round to the nearest tenth of a percent. b. Determine the original cost of a truck that has a yearly depreciation rate of 14% and is worth $12,000 after 5 yr. Round to the nearest $100.

Answer 1

a. 15.1%

b. $25,500

Explanation:

The correct depreciation expression is:

`r = 1 - ((V)/(C))^(1)/(n)`

where V is value after n year, and C is the original cost.

a.

`r = 1 - ((11000)/(18000))^(1)/(3)`

`r = 0.151392772`

r = 15.1%

b.

`r = 1 - ((V)/(C))^(1)/(n)`

`14% = 1 - ((12000)/(C))^(1)/(5)`

`0.14 = 1 - ((12000)/(C))^(1)/(5)`

`0.86 = ((12000)/(C))^(1)/(5)`

`(0.86)^5 = [((12000)/(C))^(1)/(5)]^5`

`0.470427018 = (12000)/(C)`

`0.470427018C = 12000`

`C = 25508.73898`

C = $25,500