Solve the problem.
-The yearly depreciation rate for a certain vehicle is modeled by $r = 1 - \left( \frac { V } { C } \right) ^ { 1 / n }$ , 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 $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.
A) a. 15.1% per year; b. $25,500
B) a. 77.2% per year; b. $25,500
C) a. 77.2% per year; b. $14,000
D) a. 15.1% per year; b. $14,000

Question

Quizplus · Accepted Answer

a. Substitute $V = 11000$, $C = 18000$, and $n = 3$ into the formula to find $r$. $r = 1 - \left( \frac { 11000 } { 18000 } \right) ^ { 1 / 3 }$ which simplifies to approximately 0.151 or 15.1%.b. Rearrange the formula to solve for $C$ with $r = 0.14$, $V = 12000$, and $n = 5$. This gives $C$ approximately equal to $25,500 when rounded to the nearest $100.

Solve the Problem r=1−(VC)1/nr = 1 - \left( \frac { V } { C } \right) ^ { 1 / n }r=1−(CV​)1/n

Solve the Problem $r = 1 - \left( \frac { V } { C } \right) ^ { 1 / n }$