Linearize exponential decay and curve fit to another line

I’m new to python coding and have a question regarding a set of data that I have.
The experiment I am having produces two sets of data (1) green fluorescence (signal) and (2) blue fluorescence (control). Since these are florescent signals the signal bleaches following an exponential decay and we run the assumption that the two fluorescent reporters decay at the same rate. Ideally, I would like to linearize the exponential decay of the controls and then fit that to the signal. Is that something that is possible?

Thank you for your help