Question 557336: iF THE RATE OF DEPRECIATION IS APPROX. 30% how do I find the decay factor?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! rate of depreciation per year is 30%.
that might also be equivalent to rate of decay.
b^x formula or you can use e^kx formula.
they will both provide you with the same answer.
b^x formula takes your value and raises it to an exponent for the number of time periods of your decay.
assume your original value is 100.
you have 30% depreciation / decay per year.
using the b^x factor, your formula would be:
f = p * (1 - decay factor) raised to the number of time periods.
with your numbers, that formula would be:
f = 100 * (.7)^n
if n = 0, then f = 100
if n = 1 then f = .70 * 100 = 70
if n = 2 then f = .70 * 70 = 49
etc.
using the e^kx factor, your formula would be:
first you would need to find the value of k.
you would do this by using a known decay and finding out what k is.
example:
you know that 30% decay after the first year results in 70
you would use this fact to find the value of k as follows:
70 = 100 * e^kx
e is the scientific constant of 2.718281828...
you would divide both sides of this equation by 100 to get:
.7 = e^(k*1)
you would then take the natural log of both sides of this equation to get:
ln(.7) = ln(e^k)
by the laws of logarithms, this becomes:
ln(.7) = k*ln(e)
since ln(e) = 1, this formula becomes:
ln(.7) = k
you would then find the natural log of .7 to get:
k = -.356674944
that's the value of k that would be used if you are using the e^kx formula.
let's see how both formulas work.
your starting value is 100
your decay factor is .3 per year.
you want to know the end value after 15 years.
using the b^x formula, you would do the following:
f = p * (.7)^15 which becomes:
f = 100 * (.7)^15 which becomes:
f = .474756151
using the e^kx formula, you would do the following:
f = p * e^kx
k = -.356674944
f = p * e^(-.356674944*15) which becomes:
f = 100 * e^(-.356674944*15) which becomes:
f = 100 * e^(-5.350124159) which becomes:
f = .474756151
you get the same answer either way.
the e^kx formula is used a lot in scientific studies.
the b^x formula, in this case, will provide the same answer as the e^kx formula.
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