Can you explain what is a second order exponential decay function: $$ y(x) = y_0+A_{1}e^{-\frac{x}{t_1}}+A_{2}e^{-\frac{x}{t_2}} $$

(the $t_i$, $A_i$, and $y_0$ are constants and, presumably, the "decay constants" $t_i$ are positive)?

  • Qualitatively, what is the difference between "first order" and "second order"? (A first order exponential function has the form $y(t)=y_0 + A_1 e^{-\frac{x}{t}}$.)

  • How can we estimate $t_1$ and $t_2$ from data?

  • 2
    $\begingroup$ This is also known as a biexponential function: see google.com/search?btnG=1&pws=0&q=biexponential+model $\endgroup$ – StasK Oct 16 '12 at 20:23
  • $\begingroup$ Please consult; en.wikipedia.org/wiki/Exponential_decay In order to find decay constants, fit the data with 2nd order exponential decay NLfit (Non-linear curve fit) using originlab 8.5 or higher. Good Luck $\endgroup$ – user29402 Aug 21 '13 at 17:56
  • $\begingroup$ You can model this type of function in JMP software.(non linear regression) It will come up with best estimates for all parameters $\endgroup$ – user55901 Sep 16 '14 at 17:26
  • $\begingroup$ Your second question has subsequently been answered at stats.stackexchange.com/questions/260042. It remains only to respond to the first "qualitative" question. $\endgroup$ – whuber Jan 29 at 16:12

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