Question

A car dealership creates an expression to model the value of a new car t years after it is

purchased. If the value of the car is P(0.88)', where P is the purchase price,
which statement is true?
The value of the car decreases by 12% each year.
The value of the car decreases by 88% each year.
O
The value of the car increases by 12% each year.
The value of the car increases by 88% each year.
Calculator

Answer 1

The value of car decreases by 12% each year.

Explanation:

A car dealership creates an expression to model the value of a new car t years after it is purchased and the expression is
`P(0.88)^(t)` ..... (1)

Now, if the value of the car depreciates at a rate of r% each year, then the value of the car (Say, P) will be depreciated to the value

`P' = P(1 - (r)/(100) )^(t)` ...... (2)

Now, comparing the expressions in (1) and (2), we get

`1 - (r)/(100) = 0.88`

⇒
`(r)/(100) = 0.12`

⇒ r = 12%.

Therefore, the value of the car decreases by 12% each year. (Answer)