I'm working on algorithm analysis and time complexity. I've got a homework assignment to calculate a function f(n) at time t and I want to figure out how to write it as a differential equation. Haven't taken differential equations so I'm having a tough time getting it together.
So largest size $n$ of a problem that can be solved in time $t$.
If an algorithm takes $f(n)$ microseconds to solve, whats the largest size it can solve in time $t$. $f(n) = \sqrt{n}$.
At $t=1$, $n=10^{12}$
At $t=60$, $n=36*10^{14}$
...etc
I hope I'm being concise in my question, I'm a bit frazzled at this point. Its not a matter of finding the answers, I can do that. But I want to figure out how to construct an equation to represent this.