Answer:
Step-by-step explanation:
Use the info given in the exponential equation to find the value of b, the rate of decay.
[tex]v(t)=a(b)^t[/tex] where v(t) is the value of the car after a certain number of years, t, have gone by, a is the initial value, and b is the rate of decay. We have everything we need but b:
a = 20000
v(t) = 16000 after t = 1 year:
[tex]16000=20000(b)^1[/tex] so
b = .8 Taken in context, this means that the car depreciates 20% each year. Now we can solve the problem being asked of us, which is to find the value of the car after t = 5 years:
[tex]v(t)=20000(.8)^5[/tex] which simplifies down a bit to
v(t) = 20000(.32768) so
v(t) = 6553.60, choice C.
