The yearly depreciation rate for a certain vehicle is modeled by r = 1 − ( V C ) 1 / n , 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 $12,000 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 15% and is worth $11,000 after 5 yr. Round to the nearest $100.
The yearly depreciation rate for a certain vehicle is modeled by r = 1 − ( V C ) 1 / n , 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 $12,000 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 15% and is worth $11,000 after 5 yr. Round to the nearest $100.
The yearly depreciation rate for a certain vehicle is modeled by
r
=
1
−
(
V
C
)
1
/
n
, 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 $12,000 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 15% and is worth $11,000 after 5 yr. Round to the nearest $100.
A farmer depreciates a $120,000 tractor. He estimates that the resale value V(t) (in $1000) of the tractor t years after purchase is 80% of its value from the previous year. Therefore, the resale value can be approximated by V(t) = 120(0.8)t. a. Find the resale value 5 yr after purchase. Round to the nearest $1000. b. The farmer estimates that the cost to run the tractor is $18/hr in labor, $36/hr in fuel, and $22/hr in overhead costs (for maintenance and repair). Estimate the farmer’s cost to run the tractor for the first year if he runs the tractor for a total of 800 hr. Include hourly costs and depreciation.
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