00:01
Okay, given the differential equation, dn over dt equals negative 720 over t squared minus 110, given that this equation is supposed to tell you how contaminated a stream is with bacteria.
00:24
And this is a negative differential equation.
00:26
So we're seeing that the level of contamination is lowering over time.
00:34
And that's going to be an exponential function.
00:38
Well, what we want to find is this right here as a function of t.
00:49
And the way that we do that is we solve this differential equation via separation of variables.
00:56
So you can see that this side right here is only in terms of t.
01:00
What we're going to do is bring that t over here, and then we're just going to integrate both sides.
01:06
So let's go and do that.
01:09
So we get d and equals negative 720 over t squared minus 110 dt, and then that's integrated to.
01:25
And what we're given for the limits of integration is that n, the number of bacteria, is equal to, these integrals will give us n of t equals 70010 over t...