Question

You buy a used car for $20,000. It depreciates at the rate of 21% per year. Find the value of the car after 5 years. Write the exponential decay function and solve showing your work.

a. Exponential decay function: V(t) = 20000 * (0.79)^t
b. V(5) = 20000 * (0.79)^5 ≈ $8,031.05
c. Exponential decay function: V(t) = 20000 * (0.21)^t
d. V(5) = 20000 * (0.21)^5 ≈ $352.36

Answer 1

The value of the car after 5 years is approximately $8,031.05.

Step-by-step explanation:

To find the value of the car after 5 years, we can use the exponential decay function: V(t) = 20000 * (0.79)^t. In this function, V(t) represents the value of the car after t years. We substitute t=5 into the equation to find the value after 5 years:

V(5) = 20000 * (0.79)^5 ≈ $8,031.05

Therefore, the value of the car after 5 years is approximately $8,031.05.