Question

a new car is purchased for 28,800 dollars. the value of the car depreciates at a rate of 6.6% per year. which equation represents the value of the car after 2 years?

answer
v = 28,800(0.934)(0.934)
v = 28,800(1.066)²
v = 28,800(0.066)²
v = 28,800(1 − 0.066)(1 − 0.066)(1 − 0.066)

Explanation:

Step1: Find annual value multiplier

Since depreciation rate is 6.6% = 0.066, the remaining value factor per year is $1 - 0.066 = 0.934$.

Step2: Set up 2-year value equation

After 2 years, the value is initial value multiplied by the factor twice, which is equivalent to $V = 28,800(0.934)(0.934)$.

Step3: Eliminate incorrect options

• $V = 28,800(1.066)^2$ uses a growth factor, wrong for depreciation.
• $V = 28,800(0.066)^2$ uses only the depreciation rate, not remaining value.
• $V = 28,800(1 - 0.066)(1 - 0.066)(1 - 0.066)$ calculates value for 3 years, not 2.

Answer:

$V = 28,800(0.934)(0.934)$