The thing is: a good fit at the tail end (with bad data) may very well be a very bad fit for the global (nonlinear) curve. Because you cannot linearize the data

The thing is: a good fit at the tail end (with bad data) may very well be a very bad fit for the global (nonlinear) curve. Because you cannot linearize the data or the model. Non-linear fitting is VERY hard to do well. And with pathetic data like now, it is doomed.