How to count the biggest size of the problem during some time period?
Freeman,

the answer is somewhat easy and you can do it with a simple calculator. I will assume that $\mu s$ represents a microsecond, i.e., 0.000001 second.

Let's take for example the calculus for $n^2$. You need to answer which value of $n$ makes $0.000001 f(n^2) = time\_limit$. Thus, we have:  

$0.000001 f(n^2) = 1 ~~~~~~~~\rightarrow n = 1000 ~~~~~~~~\text{(1 second)}$
$0.000001 f(n^2) = 60 ~~~~~~\rightarrow n = 7,745.97~\text{(1 minute)}$
$0.000001 f(n^2) = 3600 ~~\rightarrow n = 60,000 ~~~~\text{(1 hour)}$
$0.000001 f(n^2) = 72000 \rightarrow n = 268,328 ~~\text{(1 day)}$ 

You need to compute that for all combinations of time limit and growth factor.
Try writing a simple computer program to compute such numbers and plot all of them like the figure below. Hope you go well on your studies :)


P.S.: This figure was retrieved from here.