The initial value of your car is $20,000. After 2 years, the value is $ 15,000. a) What is the percent decrease? b) Find the value of the car at this same rate after 5 years from the initial value.

Answer 1

A = Pe^rt

in 2 years:

15000 = 20000e^2r

15 = 20e^2r

15/20 = 3/4 = .75 = e^2r

ln.75 = 2r

r = ln.75/2

r= about 14.38% yearly percentage decrease in value in years from 20K to 15K

in five years

A = 20000e^-.14.38(5)

A = 20000e^-.7192

A - 20000(.487139289)

A = $9,742.79