anonymous
  • anonymous
in 1980, your car was worth $25,000, now in 2010 your car is worth $13,000. What is the annual decay rate?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
i know decay is y=a(1=r)^x
anonymous
  • anonymous
y=Ae^(-kx) Assuming reducing balance depreciation , which is a reasonable assumption
anonymous
  • anonymous
whoops , should be y= Ae^(-kt) , for t=time in yrs

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anonymous
  • anonymous
now when t=0 , y= 25000 , so A= 25000
anonymous
  • anonymous
when t=30 , y= 13000 so 13000 = 25000e^(-30k) e^(-30k) = 13/25 -30k = ln(13/25 ) k = [ln(13/25)] / -30 = 0.0279175...
anonymous
  • anonymous
or something like that, might like to calculate k for yourself
anonymous
  • anonymous
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 )
anonymous
  • anonymous
EDIT correct value for k = 0.0217975
anonymous
  • anonymous
so this means that every year the car losses 2.17975% of its previous years value
anonymous
  • anonymous
thanks

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