# Efficiency of a simple algorithm

I am kind of confused on this problem although it seems extremely simple. So I am supposed to determine the largest size n of a problem that can be solved in time t, assuming that the algorithm takes f(n) seconds to solve a problem of size n. Given is the function: n^2+100 for 1 minute.

Normally if this was n^2 I could just put in n = 7 (if rounded).

But for n^2+100 there is no real answer. I know that if n gets sufficiently large the 100 can just be ignored.

So is the answer just N/A, i.e. the algorithm cannot be solved in 1 second even with size 0?

Thanks a lot for any responses.

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What does "algorithm takes f(n) seconds of a function n^2+100 for 1 minute" mean? –  Vedran Šego Sep 15 '13 at 0:44

If you mean that a problem of size $n$ takes $n^2+100$ seconds, you are correct that even a problem of size $1$ takes $101$ seconds, which is greater than one minute.