Think of a line graph where the line stays somewhat flat and low to the ground for a while (but still upsloping, nondecreasing) and then starts to arc up.
I'm trying to figure out a way to "characterize" these kinds of lines (when does this "hard arc" point occur, how hard is the arc, etc). Please ask questions if I am not being clear.
I tried to draw an example of what I mean https://i.stack.imgur.com/Z7HWe.png
For example I should be able to have a model equation that describes a line like this, and based on whatever such coefficient I can say "This coefficient means the arc starts to occur sooner" or "This coefficient means the arc, when it occurs, is rather strong." Does this make sense?
These are graphs of $e^x$. You can see at x=0 the graph starts raising and after 10 it's just increases drastically like a vertical line.
So, for $Ae^{x-c}$ the graph will start shooting upwards at $x-c=0$ C shifts graph from one place to other on X-axis.
and the A controls the amplitude of the function and B controls the argument of function $f(x)$ , so it can even reverse the whole curve too (b<0).