00:01
Here, we're given a differential equation where the derivative of p with respect to time is 1 .5p times 1 minus p over 4 ,700.
00:09
And i want to know for part a for what values of p is the population increasing? that means its derivative is positive.
00:16
So i'm going to treat this kind of like the first derivative test.
00:19
I'm going to find out when is the derivative positive.
00:22
Well, we are given the derivative.
00:24
So if p is equal to zero or if p is equal to, let's see, that would be 4 ,700.
00:31
Either those are basically critical points.
00:34
So if i see what's happening around that, so 0 and 4 ,700, those are the only places it can change direction.
00:41
So if i plug in some number here, say 2 ,000, i don't care what it is, well, it's going to be one minus a number that is smaller than 1, so it is going to be positive here...