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.
[tex]y=a\cdot b^x[/tex], 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.
[tex]7.25\%=\frac{7.25}{100}=0.0725[/tex]
Upon substituting our given values in above formula we will get,
[tex]y=\$28,000\cdot(1-0.0725)^5[/tex]
[tex]y=\$28,000\cdot(0.9275)^5[/tex]
[tex]y=\$28,000\cdot 0.686387856528418[/tex]
[tex]y=\$19218.8599\approx \$19219[/tex]
Therefore, the value of car 5 years after it is purchased will be $19219.
