00:01
Okay, this question is addressing our logistic growth equation.
00:15
And so we're looking at population growth, population size.
00:19
So let's write this equation out and identify then the different parts so we can see what's happening with it.
00:41
So we're looking at the growth of a population at a given time.
00:47
So change in population over time.
00:52
Where r is our intrusic rate of growth.
01:05
So it's different for different populations.
01:07
Our n is then our population size at that given time.
01:17
So that comes up here.
01:19
And our k is our carrying capacity.
01:24
So pretty much the maximum number of individuals that can be supported for that given population in that given environment at that time.
01:44
And our graph for this is then our graph that starts out, it goes out slow, then it starts to increase exponentially, and then it's going to level off.
02:06
So our sigmoid shape, there's our k, right, and there is fluctuation around that k.
02:13
In the line.
02:14
But we have number of individuals in the population, and this is the time.
02:26
So zero, say, to 20 years.
02:30
So zero up to 100 individuals.
02:34
Okay.
02:35
So what we see is that our population starts out slow because we only have a few number of individuals.
02:46
It starts all is that slow? then once we get past those lower numbers, it starts to increase greatly, and then the rate is going to obviously stabilize off because it's going to hit that carrying capacity...