00:01
This is a two -part question.
00:02
First, we're told that the cost, c, in dollars, to remove p percent of an invasive species of fish, is given by c of p equals 1770p over 100 minus p, where p can be between 0 and 100.
00:21
And part a of this question is to find and interpret c of 25 and c of 95.
00:29
So see if 25, you just plug 25 into the equation and you'll get 590.
00:36
You plug 95 in to the equation or the formula, sorry, the function.
00:42
You'll get 33 ,630.
00:46
So what this means is that it costs $590 to remove 25 % of the fish.
01:02
And it costs $33 ,630 to remove 95 % of the fish.
01:16
That's what this tells us.
01:19
And part b of this first question is, what does the vertical asymptote at p equals 100 mean within the context of the problem? so the vertical asymptote at p equals 100 means for us.
01:40
So just to get a sketch of the graph here, there's this vertical asymptote, 100.
01:52
As you get close, you go up and up and up and up.
01:55
It tells us that basically the more fish you remove, the more fish we remove, the more it costs.
02:15
And we can never actually remove 100 % of the invasive fish species.
02:28
If we were allowed to remove all 100 % of this fish population, then there would just be some cost associated to that process.
02:37
The fact that we have an asymptote is we can get really, really close to getting rid of 100%, but we can never quite get there.
02:44
And the closer we get, the more and more and more costs.
02:49
Okay.
02:50
So part c of this first question, what percentage of the fish can you remove for $400 ,000? sorry, for $40 ,000.
02:58
So we just want to set this cost function equal to $40 ,000 and solve for p.
03:04
We want to figure out what value of p gives the cost of $40 ,000...