C=80,000p/(100-p)

A)what happens of the company tries to remove 100 percent of the pollutants? Will it work or will it cost too much?
B)draw a diagram to show what the consequences of the last question would be. Label the verticals asymptote(s) and analyze their impact on the company's expense.

I know that trying to remove 100% will cost too much but I don't know how to show that in a graph, please help! And thanks in advance!

your equation "falls apart" when p = 100

because you would be dividing by zero
So mathematically, the cost would be infinitely large
(that is, it is not possible)

look at this graph and see what happens at p = 100
http://www.wolframalpha.com/input/?i=plot+C%3D80%2C000p%2F%28100-p%29+%2C+0+%3C+p+%3C+110

at p = 100 you would have a vertical asymptote
you can get as close to p = 100 as you want and still have an answer. But the closer you get the larger the value of C

e.g. let p = 99
C = 80000(99)/(100-99)
= $79,200,000

let p = 99.9
C = 800000(99.9)/.1
= $ 799,200,000

To determine what happens if the company tries to remove 100 percent of the pollutants, let's substitute p=100 into the formula C=80,000p/(100-p):

C = 80,000 * 100 / (100 - 100)
C = 80,000 * 100 / 0

As we can see, this calculation is undefined because of the division by zero. Therefore, trying to remove 100 percent of the pollutants is not possible, and it does not make sense to evaluate the cost in this scenario.

To demonstrate this on a graph, let's graph the function C=80,000p/(100-p):

First, let's find the vertical asymptote(s) of the graph. Vertical asymptotes occur when the denominator of a rational function becomes zero. In this case, the denominator is (100-p). Hence, the vertical asymptote occurs at p=100.

Next, let's plot the graph considering values of p from 0 to 99. This will give us an idea of the cost for different pollution removal percentages:

When p=0, C=80,000(0)/(100-0) = 0.
When p=1, C=80,000(1)/(100-1) ≈ 800.
When p=2, C=80,000(2)/(100-2) ≈ 1600.

Similarly, you can calculate and plot more values until p=99.

From the graph, as p gets closer to 100, the cost (C) increases and approaches infinity. This visually represents the cost becoming unreasonably high if the company aims to remove 100 percent of the pollutants.

To summarize, removing 100 percent of the pollutants is not possible, as indicated by the undefined result when p=100. The graph illustrates that the cost increases significantly as the removal percentage approaches 100, making it impractical for the company.

To answer these questions, we will analyze the given equation and understand its behavior.

A) What happens if the company tries to remove 100 percent of the pollutants?

In the given equation, C = 80,000p/(100-p) represents the cost (C) based on the percentage of pollutants removed (p).

As we can see, when p = 100, the denominator (100 - p) becomes zero. Division by zero is undefined, so the equation is not defined for p = 100. Therefore, it is not possible to remove 100 percent of the pollutants.

B) To understand the consequences, let's plot the graph of the equation:

To analyze the graph of C = 80,000p/(100-p), we can plot some points and draw the curve. Here's how we can do it:

Let's start by evaluating the equation for different values of p:

For p = 0%, C = 0
For p = 10%, C = 88,888.89
For p = 20%, C = 133,333.33
For p = 30%, C = 200,000.00
For p = 40%, C = 333,333.33
For p = 50%, C = 800,000.00
For p = 60%, C = 2,000,000.00
For p = 70%, C = 7,000,000.00
For p = 80%, C = 40,000,000.00
For p = 90%, C = 800,000,000.00
For p = 99%, C = 80,000,000,000.00

Plotting these points and connecting them with a smooth curve, we get the graph as shown below:

^
|
90% / .
| .
| .
| .
/'
--------------------
80% \
.'
.
.
'
|
|
|-------------
50% 70% 80% 90% 99%

From the graph, you can observe that as p approaches 100%, the cost (C) tends to infinity. This means that the cost of removing pollutants becomes significantly high as we get closer to 100% removal. In other words, it will cost too much for the company to remove 100% of the pollutants.

The vertical asymptote of the graph occurs at p = 100, which means there is no cost associated with removing 100% of the pollutants. This reinforces the fact that it is not possible to remove 100% of the pollutants.

I hope this helps! Let me know if you have any further questions.