I am trying to figure out how to characterize the decay of $f(x), g(x), h(x)$ in the graphs below. I think I don't have a solid grasp on what exponential and algebraic decay really mean.
What I think they mean:
A function (or set of data) decays exponentially if $f(x)$ goes to $0$ as some exponential function of $x$. Similarly, the decay is algebraic if $f(x)$ goes to $0$ as a function of some polynomial function of $x$.
Now, despite this, I'm not sure how I would classify the below. Here's what I think:
$f(x)$ obviously displays some sort of "split behaviour". Some of the function values are basically zero, but the rest of them certainly follow some trend. The fact that it's a straight line on the log-log plot makes me think that the decay is not exponential. Does this mean that it's algebraic?
$g(x)$ I'm not quite sure what to make of. It has some concavity on both plots, so I don't know how to interpret that.
$h(x)$ looks to me like a typical case of exponential decay.
Any help would be hugely appreciated.