Question

Depreciation A car sells for $28,000.The car

Answer 1

Answer:

$V(t)=28,000(0.75)^t$.

$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 $y=a(b)^x$, 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 $b=\frac{3}{4}=0.75$.

Therefore, our required function would be $V(t)=28,000(0.75)^t$.

To find the value of car after 4 years, we need to substitute $t=4$ in our function as:

$V(4)=28,000(0.75)^4$

$V(4)=28,000(0.31640625)$

$V(4)=8859.375$

Therefore, the value of the car after 4 years would be $8859.375.