Question

Doug bought a new car for $25,000. He estimates his car will depreciate, or lose value, at a rate of 20% per year. The value of his car is modeled by the equation V = P(1 – r)t, where V is the value of the car, P is the price he paid, r is the annual rate of depreciation, and t is the number of years he has owned the car. According to the model, what will be the approximate value of his car after 4 and one-half years?

Answer 1

Answer:

These are the values you have:

P = 25000 (original car value)

r = 20% or .2 rate of decrease

t = 4 1/2 or 4.5

Plug these into the equation: V=25000(1-.2)^4^.^5 = 9159

Answer 2

Concept Introduction:-

The process by which the value of something reduces over time is known as Depreciation.

Given Information:-

We have been given that Doug bought a new car for $25,000$. He estimates his car will depreciate, or lose value, at a rate of $20%$% per year.

To Find:-

We have to find that the approximate value of his car after $4$ and one-half years.

Solution:-

According to the problem

Given equation is:

$\begin{aligned}&V=P(1-r)^{t} \\&\mathrm{P}=\ 25000 \\&\mathrm{r}=20 \% \text { or } 0.20 \\&\mathrm{t}=4.5 \text { years }\end{aligned}$

So, equation becomes:

$\begin{aligned}&25000(1-0.20)^{4.5} \\&=25000(0.80)^{4.5} \\&=\ 9159\end{aligned}$

Final Answer:-

The approximate value of the car will be $\ 9159$.