Two term exponential decay. Coefficient interpretation.

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Hello, I'm a noob so please be patient.
I have some data which arise from a biological process:
time = [2.6666 2.9547 3.0731 3.1745 3.5116 4.6746 5.0286 5.0792 5.8882 6.1748 6.9502 7.2198 7.6918 8.0963 8.9560 9.6134 10.0179 11.7878 12.1586 13.5239 16.5748 18.2098 18.5301 19.1032 23.0643 24.4633 25.3398 26.0983 27.2277 27.9525 28.4581 29.8234 31.0033 31.6607];
and
thresh = [ -0.1001 -0.4324 -0.6791 -0.9764 -1.2419 -1.4490 -1.6542 -1.7217 -1.7448 -1.7901 -1.8163 -1.8351 -1.8534 -1.8564 -1.8742 -1.8886 -1.9057 -1.9421 -1.9618 -1.9731 -1.9788 -1.9962 -2.0021 -2.0111 -2.1014 -2.1091 -2.1330 -2.1677 -2.1961 -2.2011 -2.2061 -2.2665 -2.3105 -2.3524];
I think this data can be well explained by a two term exponential decay model, since there is a fast period of decay followed by a slower period. Curve fitting using cftool looks good to me but I'm having trouble with interpreting the resulting coefficiants a, b, c and d. I've not really gone beyond linear regression in my understanding of fitting lines to data, so would someone kindly be able to help me out here?
It seems like a is probably the plataeu point where one exponential ends and the other begins, b could be the rate of change for the fast decay, c seems to be where the slow decay crosses the x axis and d is maybe the rate of change for the slow decay?
Any help, advice or information would be much appreciated. The explanation of exponential decay in the Matlab help wasn't super useful for coefficient interpretation.
Many thanks in advance and sorry for such a basic question. MP.

Answers (1)

Star Strider
Star Strider on 3 Jul 2015
Ideally, you have a mathematical expression for the process you’re modeling, for instance a compartmental model, enzyme kinetics, or something similar. I would use that model to define the objective function. Then the parameters you’re estimating will have obvious physical relevance.

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