Question

in 1980, your car was worth $25,000, now in 2010 your car is worth $13,000. What is the annual decay rate?

Answer 1

i know decay is y=a(1=r)^x

Answer 2

y=Ae^(-kx)

Assuming reducing balance depreciation , which is a reasonable assumption

Answer 3

whoops , should be y= Ae^(-kt) , for t=time in yrs

Answer 4

now when t=0 , y= 25000 , so A= 25000

Answer 5

when t=30 , y= 13000

so 13000 = 25000e^(-30k)

e^(-30k) = 13/25
-30k = ln(13/25 )
k = [ln(13/25)] / -30 = 0.0279175...

Answer 6

or something like that, might like to calculate k for yourself

Answer 7

now k is defined at the decay rate as a decimal

because if you differentiate , y= Ae^(-kt)

you get dy/dt = -k y , ie minus sign means its decreasing , and the factor of k is the rate ( as a decimal )

Answer 8

EDIT correct value for k = 0.0217975

Answer 9

so this means that every year the car losses 2.17975% of its previous years value

Answer 10

thanks