00:01
So for this problem, we have two animals, have a predator -prey relationship.
00:07
We can see their population over time.
00:09
So if we have the number in a given area to be n of t equals 250 -90 -t, so it's going to oscillate, obviously, plus 500, n is the number of prey, t is the number of years since 1990.
00:23
So we want to know the population of the prey animals in 1990.
00:28
So that's going to be no -zero, which means this.
00:31
Whole thing goes to zero, and we're just left with 500.
00:35
So that's the population.
00:37
The maximum number is going to be found if we take n prime of t and maximize this.
00:43
So take the derivative, set it equal to zero, and find where that critical point is.
00:48
Another option would be for you to just graph this function and look for the maximum.
00:53
We can also consider the minimum as well doing the same method...