Select a "mature" curve that best matches the slope of a new "immature" curve
This seems more like a mathematical problem than a coding problem, but I do have a solution.
If you want to find how similar two curves are, you can use box-differences or just differences.
You calculate or take the y-values of the two curves for each x value shared by both the curves (or, if they share no x-values because, say, one has even and the other odd values, you can interpolate those values).
Then you take the difference of the two y-values for every x-value.
Then you sum up those differences for all x-values.
The resulting number represents how different the two curves are.
Optionally, you can square all the values before summing up, but that depends on what definition of "likeness" you are using.
I have a multitude of mature curves (days are plotted on X axis and data is >= 90 days old so the curve is well developed).
Once a week I get a new set of data that is anywhere between 0 and 14 days old.
All of the data (old and new), when plotted, follows a log curve (in shape) but with different slopes. So some weeks have a higher slope, curve goes higher, some smaller slope, curve is lower. At 90 days all curves flatten. 
From the set of "mature curves" I need to select the one whose slope matches the best the slope of my newly received date. Also, from the mature curve I then select the Y-value at 90 days and associate it with my "immature"/new curve.
Any suggestions how to do this? I can seem to find any info. 
Thanks much!