We understand the exponential function to constantly grow, which we consider bad for a problem. By constantly growing I mean the ratio $\frac{f(n+1)}{f(n)}$ never tends to 1, where $f(n)$ is the exponential function.
However, when this ratio tends to 1, we can roughly say that as problem size increases by a small amount say O(1), then the time taken does not change by a large amount. Then why did we choose polynomials as a natural measure of easiness? Why don't we want the ratio $\frac{f(n+c)}{f(n)}$ of the time complexity to tend to 1, when $n \rightarrow \infty$. Note that $c = O(1)$ is any positive constant.
