Question

calculate the value of the car after 5 years: $2847.66
question #2
kathy plans to purchase a car that depreciates(loses value) at a rate of 14% per year. the initial cost of the car is $21,000. which equation represents the value, v, of the car after 3 years?
(a) $v = 21,000(0.14)^3$
(b) $v = 21,000(0.86)^3$
(c) $v = 21,000(1.14)^3$
(d) $v = 21,000(0.86)(3)$

Explanation:

Step1: Identify depreciation rate

The car loses 14% value yearly, so the remaining value percentage is $100\% - 14\% = 86\% = 0.86$.

Step2: Use exponential decay formula

Exponential depreciation formula is $V = P(1-r)^t$, where $P=\$21,000$, $r=0.14$, $t=3$. Substitute values: $V = 21,000(0.86)^3$.

Step3: Match to options

Compare the derived equation to the given choices.

Answer:

(b) $V = 21,000(0.86)^3$