00:01
All right, here we have which is the smallest value of n such that an algorithm whose running time is 256n squared, 256n squared, runs faster than an algorithm whose running time is 2n or 2 to the n.
00:18
So what we want is what this means is if this is running faster, then that means it takes less time.
00:25
So we want to see what is the value of n that makes this inequality true.
00:31
So the thing to do is just to test different values of n and just start kind of zeroing in.
00:40
There's not really an algebraic method to do this by.
00:42
So we're going to say what happens when n equals 1.
00:45
Well, then we have just 256 is less than 2, which is not true.
00:51
So maybe what we can do is say, ok, what about if n equals 10? well, then we can say 256.
00:57
What we can do is open up our graphing calculator, which i'm going to do presently.
01:01
256 times 10 squared.
01:03
So 256 and then parentheses 10.
01:07
Let me try that again.
01:09
256 times 10 now raised to the 0.
01:15
Wait, yeah, that's right, to the second power.
01:18
That's 25 ,600.
01:20
So that gives us 25 ,600.
01:25
And then 2 to the 10th, right? 2 raised to the 10th is 1024.
01:31
So that is 1024, right? so obviously, this is growing pretty quickly because it's being multiplied by 256.
01:42
So let's try n equals 20.
01:44
What what happens when n equals 20? well, i'm going to do the same thing.
01:49
I'm going to say, okay, 256 times 20 squared...