How much time would be needed to compute an algorithm with time complexity $O(n^k)$?
An algorithm has time complexity $O(n^k)$ if there exists a constant $C&gt;0$ such that the number of operations that the algorithm performs in the RAM model on an input of length $n$ is at most $Cn^k$.

There are several reasons why this doesn't allow you to determine how much time the algorithm will take on a given machine for a given value of $n$:


$Cn^k$ is only an upper bound.
We don't know the value of $C$.
Your machine differs from the abstract model of computation used to analyze the algorithm.


Therefore the only way to really know how much time a certain algorithm would take is to code it and empirically measure its running time.

What good is asymptotic analysis, then? The abstract machine is a reasonable model of real computers, so it is likely that the running time will scale like $n^k$ (assuming $O(n^k)$ is a tight upper bound). If $k$ is large, then likely the algorithm isn't practical. So asymptotic analysis allows you to compare different algorithms on paper rather than in practice. Of course, sometimes this comparison will result in the wrong conclusion. This is the case for fast matrix multiplication, for instance.