Question

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

Answer 1

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 $P(0.88)^{t}$ ..... (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

$P' = P(1 - \frac{r}{100} )^{t}$ ...... (2)

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

$1 - \frac{r}{100} = 0.88$

⇒ $\frac{r}{100} = 0.12$

⇒ r = 12%.

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