Fit family of curves

I have 30 sets of data. Each data has an exponential decay y=(a-b)*exp(-c*x)+b. I used lsqcurve to find the parameters but I really need a general model of that family of curves. how can I do it?

[Star Strider]

Do they all have the same number of data pairs (are they all sampled at the same number of x points), or do the number of (x,y) observations differ among the 30? (They don’t all have to be sampled at the same x values.)