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Hello, I'm working on this Mathematica assignment, just basic tutorial-type stuff (you can ignore the details about pyrene, not important), and the fit on this function won't converge. Someone in my class said it converged fine, so I was wondering if anyone notices any errors in my work. Alternatively, can you think of any alternative ways to express the function?

Thanks!

3. Formation and Decay of Pyrene Excimer in Solution

The traces for pyrene fluorescence (see Experiment 3) show a fast rise and a slower fall processes which correspond to a complex kinetic of the formation and decay of the pyrene excimer in solution. The evolution of the excimer fluorescence intensity I(t) in time t can be described by the following equation:

I(t) = -Ae

Data are provided in a file “emission_data” with time given in the first column, while the fluorescence intensity given in the second column.

REPORT:

(1) Find coefficients A, B, ka and kb. Estimate standard error and confidence levels for these parameters. Hint: see Mathematica help menu for function NonlinearModelFit.

(2) Provide plot of data with the superimposed fit function

Mathematica knowledge

See attached screenshot.

I can get 3/4 coefficients, but I don't know if they're correct due to the fourth one failing to converge, and I can't make the plot without all coefficients!

Thanks!

## Homework Statement

3. Formation and Decay of Pyrene Excimer in Solution

The traces for pyrene fluorescence (see Experiment 3) show a fast rise and a slower fall processes which correspond to a complex kinetic of the formation and decay of the pyrene excimer in solution. The evolution of the excimer fluorescence intensity I(t) in time t can be described by the following equation:

I(t) = -Ae

^{-kat}+Be^{-kbt}Data are provided in a file “emission_data” with time given in the first column, while the fluorescence intensity given in the second column.

REPORT:

(1) Find coefficients A, B, ka and kb. Estimate standard error and confidence levels for these parameters. Hint: see Mathematica help menu for function NonlinearModelFit.

(2) Provide plot of data with the superimposed fit function

## Homework Equations

Mathematica knowledge

## The Attempt at a Solution

See attached screenshot.

I can get 3/4 coefficients, but I don't know if they're correct due to the fourth one failing to converge, and I can't make the plot without all coefficients!