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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.
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Respuesta :

Answer:

The value of car decreases by 12% each year.

Step-by-step 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 [tex]P(0.88)^{t}[/tex] ..... (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

[tex]P' = P(1 - \frac{r}{100} )^{t}[/tex] ...... (2)

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

[tex]1 - \frac{r}{100} = 0.88[/tex]

⇒ [tex]\frac{r}{100} = 0.12[/tex]

⇒ r = 12%.

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

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