00:01
All right, so for this question we are given a multivariable function p.
00:05
It's given by the equation here.
00:07
This value p is percentage of fish intolerant to pollution.
00:14
Then we have w is percentage of wetland area, r is percentage of residential, and a is percentage of agricultural area that surrounds the swamp where these fish are.
00:28
Okay, so there are a couple parts to this problem.
00:32
The first part wants us to use the function to estimate the percentage of fish intolerant to pollution.
00:39
In other words, they want us to evaluate p if 5 % of the land is classified as wetland.
00:50
In other words, if w is equal to 5, 15 % is residential, and 0 % is agricultural.
01:06
So we have the values substituted in for w, r, and a.
01:13
So we can plug those into the main equation for the function, which gives us this.
01:29
Let's go ahead and put this into a calculator.
01:35
When you do, you should get exactly 8 .7%.
01:41
Okay, what else do we want? the next question says, what is the maximum percentage of fish intolerant to pollution? so in other words, we're looking for a maximum value for p.
01:56
And the thing that really makes this work out is the fact that w, r, and a all represent percentages, which means by default, each one of these variables must be non -negative, which is really good then, because what that means is that each of the terms that appear in the p function are always going to be non -positive.
02:25
And what this does is it guarantees a maximum when all three percentages are 0.
02:32
So in other words, the maximum value for p is going to be when all three are 0, which will equal 48%.
02:52
The third part is asking to develop two scenarios that will drive the percentage of fish that are intolerant to pollution to 0.
03:02
What does that mean? it means we need to construct values for the variables such that p equals 0.
03:13
So we're going to go ahead and construct the simplest way that this can happen...