Fit an exponential decay function to connect two separate parts of a curve.

Hi,

I have a curve which stops and re-starts, with an intermittent part being missing. At the missing part, my data can be described with a standard exponential decay of the form A=Data(i)*exp(-b*t), where Data(i) is the last point of the first part of the curve and t is the time points of the missing segment. I basically want to fit an exponential decay function in the missing part, to create a full profile for this curve (which will be later on mathematically modelled to derive different metrics). Any ideas which would be the best way to do so? At the moment I am attempting to create a straight line to connect the two separate parts and then fit an exponential function in this straight line, but I am not sure if there would be another quick way to do so in Matlab. I am attaching an example.