00:01
So for this problem, we're going to look at logistic model equations, and we're not just going to define it, but we're going to discuss what each parameter actually does.
00:08
So let's say we have our function.
00:10
We'll call it a function of time because usually that's what we are dealing with.
00:17
And it's going to be written as l.
00:21
Usually we write l because it's the limit, as we'll soon see, over 1 plus b, e to the negative kp.
00:30
There's a lot of different ways to write this, but this is one.
00:33
And we see that there's a lot of different parameters.
00:36
So the first thing that we want to do if we're trying to actually find the model and write the model is the kind of two extremes.
00:45
What's going to happen when time is zero and what's going to happen when time is infinite? so as it goes on forever.
00:54
So when time or whatever it is, usually time is zero, we see that this whole thing becomes one right here.
01:03
This is going to become b, and now we have 1 plus b, so l over 1 plus b, that's going to be what we start off with.
01:16
Then let's say time goes to infinity.
01:19
Well, if time goes to infinity, this whole thing goes to zero, right here, so we get 1 plus 0, which is 1, so then we reach l, our limit.
01:27
That's why it's called the limit.
01:31
So what we end up seeing is if we're trying to model this, we want to start off by looking at where t goes to infinity, because if we do that, then we'll see that that will give us our l value.
01:45
And then if we now have our l value, we can then plug in a different t value and then find the b value.
01:55
Preferably, we could plug in zero, and that would allow us to find a little bit easier...