Answer:
$14500
Step-by-step explanation:
For a car with an initial value [tex]A_0[/tex], its value, A(t) after time t for which it depreciates by period k with a decay rate of r is given is:
[tex]A(t)=A_0 \cdot r^{t/k}[/tex]
If the value of the car depreciated by [tex]\dfrac{1}{2}[/tex] every four years, then the value of the car at any time t is defined by the function:
[tex]A(t)=41000(0.5)^{t/4}[/tex]
We want to determine the value of the car 6 years after it was purchased.
When t=6
[tex]A(6)=41000(0.5)^{6/4}\\=\$14495\\\approx \$14500 $(to the nearest hundred dollars)[/tex]
