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anonymous

  • 5 years ago

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

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  1. anonymous
    • 5 years ago
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    i know decay is y=a(1=r)^x

  2. anonymous
    • 5 years ago
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    y=Ae^(-kx) Assuming reducing balance depreciation , which is a reasonable assumption

  3. anonymous
    • 5 years ago
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    whoops , should be y= Ae^(-kt) , for t=time in yrs

  4. anonymous
    • 5 years ago
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    now when t=0 , y= 25000 , so A= 25000

  5. anonymous
    • 5 years ago
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    when t=30 , y= 13000 so 13000 = 25000e^(-30k) e^(-30k) = 13/25 -30k = ln(13/25 ) k = [ln(13/25)] / -30 = 0.0279175...

  6. anonymous
    • 5 years ago
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    or something like that, might like to calculate k for yourself

  7. anonymous
    • 5 years ago
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    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 )

  8. anonymous
    • 5 years ago
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    EDIT correct value for k = 0.0217975

  9. anonymous
    • 5 years ago
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    so this means that every year the car losses 2.17975% of its previous years value

  10. anonymous
    • 5 years ago
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    thanks

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