Actually, exponentially either gets much faster, or much slower, when moving up or down in the function. It would actually get much slower, in this case, as you lose training. Once it hits a certain point, say 20 training, it will be so slow as to effectively not be going down anymore. Leaving a unit that is still able to fight in combat, but not nearly as effective as one with 70 training.
You mean something like this:
http://www.wolframalpha.com/input/?i=graph+0.8%2F%28e^%28%28x-10%29%2F2%29%2B1%29%2B.2%2C+x+from+0+to+30+y+from+0+to+1
With x being days and y being training? It could work, but it still clearly has a threshold after which it goes down.
A power law would be like this:
http://www.wolframalpha.com/input/?i=graph+0.4*%28%281-.01*x^2%29%2F%281%2B.01*x^2%29%29%2B.6%2C+x+from+0+to+30+y+from+0+to+2
This one starts having an an effect quicker, and the effect is small but noticeable. It doesn't speed up very much. After a long time, you just reach the floor.
(Note: copy the full link to see, I'm not sure how to force the parse to recognize it)
