Different results for same equation in curve fitting

Why is custom fitting not the same as the exponential default one as shown in the picture? The data fits nicely when I use the 'exp2' instead.

I'm relatively new to MATLAB and this is quite baffling to me as i am unable to use a custom equation as it simply does not fit.

[Ayushi Sharma]

This is for reference, same equation, different fitting results

[dpb]

Starting guess chosen between the two.

While I've not tried to delve into the bowels, the prepackaged exponential model probably has a customized technique to estimate the starting values whereas (I think) the custom model just starts with a random guess.

NB: The sign of a and b between the two is reversed; to get the overall negative value, one has to be negative and larger than the other; where the initial guess starts will determine which is which as the iterations continue.

While the result looks decent for the latter NB the two coefficients a and c

a = -4E12 +/-3E20(!!!)

or the CV (coefficient of variation) for the coefficient is 7.5E7 -- a highly imprecise value.

For data that looks like the above, why would you choose the exp2 model and not exp1, however? No sign of there being a competing exponential in there that I can see.

[Ayushi Sharma]

I already have a custom equation:

a*exp(-x/T) +c*(T*(exp(-x/T)-1)+x)

I need to find the value of constant 'c'

In the csv attached:

y = dv

and x= t