Exponential asymptote
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Hi,
I used an exponential function to fit my data and I'd like to know where the function reaches a plateau. How do I calculate that?
Here's the function I used: y = a1+a2*exp(-a3*t)
I also tried a power function : y = a*b^t
Thanks in advance!
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Sean de Wolski
2011-5-26
I'm excited to read John's response if he sees this.
Andrew Newell
2011-5-26
Google "identifying asymptotes"
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Walter Roberson
2011-5-26
a1+a2*exp(-a3*t) plateaus at the point where a2*exp(-a3*t) is less than eps(a1) . You can work backwards from there:
a2*exp(-a3*t) = eps(a1)
exp(-a3*t) = eps(a1)/a2
-a3*t = ln(eps(a1)/a2)
t = -ln(eps(a1)/a2)/a3
You might need to tweak this calculation if a1 or a2 are negative.
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Walter Roberson
2011-5-26
That is the time t at which the plateau is reached. If your maximum t for your data is less than that number, your function has not reached the plateau.
You would know if you had reached a plateau because all of the function values after that would be identical (to within round-off error)
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