Answer:
[tex]V(t)=28,000(0.75)^t[/tex].
$8859.375
Step-by-step explanation:
Please find the attachment for the function.
We have been given that a car sells for $28,000.The car depreciates such that each year it is worth 3/4 of its value from the previous year. We are asked to find the model for the value V of the car after t years.
We know that an exponential function is in form [tex]y=a(b)^x[/tex], where,
a = Initial value,
b = Growth or depreciation rate.
Since each year the car worth 3/4 of its value from the previous year, so its value is depreciating and [tex]b=\frac{3}{4}=0.75[/tex].
Therefore, our required function would be [tex]V(t)=28,000(0.75)^t[/tex].
To find the value of car after 4 years, we need to substitute [tex]t=4[/tex] in our function as:
[tex]V(4)=28,000(0.75)^4[/tex]
[tex]V(4)=28,000(0.31640625)[/tex]
[tex]V(4)=8859.375[/tex]
Therefore, the value of the car after 4 years would be $8859.375.
