Piecewise curve fitting polynomial data

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Hello all. I am curve fitting time series data using polyfit() and it works well for most of my data sets. I have noticed, however, that some data sets begin hyperbolic and move to exponential so as to best fit to two separate equations. What is simple way to fit my data to two different curve equations using Sage? Is there a good mathematical or programmatic method of determining when a data set is best served by piecewise curve fitting? Currently, I can only determine that empirically once the curve is plotted along with the data points.

Natasha