Exponential asymptote

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!

[Sean de Wolski]

I'm excited to read John's response if he sees this.

[Andrew Newell]

Google "identifying asymptotes"

Answer 1

[Walter Roberson]

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.

[Walter Roberson]

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)