Question

A new car is purchased for $41,000\$41,000$41,000 and over time its value depreciates by one half every 4 years. What is the value of the car 6 years after it was purchased, to the nearest hundred dollars?

Answer 1

$14500

Explanation:

For a car with an initial value
`A_0`, its value, A(t) after time t for which it depreciates by period k with a decay rate of r is given is:

`A(t)=A_0 \cdot r^(t/k)`

If the value of the car depreciated by
`(1)/(2)` every four years, then the value of the car at any time t is defined by the function:

`A(t)=41000(0.5)^(t/4)`

We want to determine the value of the car 6 years after it was purchased.

When t=6

`A(6)=41000(0.5)^(6/4)\\=\$14495\\\approx \$14500 $(to the nearest hundred dollars)`