Question

Alex purchased a new car for 28,000. The cars value depreciates 7.25% each year. What will be value of the car 5 years after it is purchased? Round your answer to the newest dollar

Answer 1

Answer:

$19219.

Step-by-step explanation:

We have been given that Alex purchased a new car for 28,000. The cars value depreciates 7.25% each year.

We will use exponential decay function to solve our given problem.

$y=a\cdot b^x$, where,

a = Initial value,

b = For decay b is in form (1-r), where r represents decay rate in decimal form.

Let us convert our given rate in decimal form.

$7.25\%=\frac{7.25}{100}=0.0725$

Upon substituting our given values in above formula we will get,

$y=\ 28,000\cdot(1-0.0725)^5$

$y=\ 28,000\cdot(0.9275)^5$

$y=\ 28,000\cdot 0.686387856528418$

$y=\ 19218.8599\approx \ 19219$

Therefore, the value of car 5 years after it is purchased will be $19219.

Answer 2

If depreciation is 7.25% per year, then the common factor is (1-0.0725), or 0.9275.

Thus, the car's value after 5 years will be:

V = $28000(0.9275)^5 = $28000(0.6864) = $19218.86, or (to the nearest dollar) $19218 (answer)