Question

In Palo Alto, California, a government agency ordered computer-related companies tocontribute to a pool of money to clean up underground water supplies. (The companieshad stored toxic chemicals in leaking underground containers.) The formula = 2/100− a) What percentage of the contaminants can be removed for $2 million?b) What percentage of the contaminants can be removed for $8 million?c) Is it possible to remove all of the contaminants? Explain the reasoning behind youranswer.

Answer 1

a) 50%

b) 80%

c) It is not possible to remove all the contaminants

Explanation:

We have the following function:

`=(2x)/(100-x)`

Where C would be the cost and x the percentage of removal, therefore:

a)

`\begin{gathered} C=2 \\ \text{ replacing} \\ 2\cdot(100-x)=(2x)/(100-x)\cdot(100-x) \\ 2\cdot(100-x)=2x \\ 200-2x=2x \\ 4x=200 \\ x=(200)/(4) \\ x=50\text{\%} \end{gathered}`

b)

`\begin{gathered} C=8 \\ \text{ replacing} \\ 8=(2x)/(100-x) \\ 8\cdot(100-x)=2x \\ 800-8x=2x \\ 10x=800 \\ x=(800)/(10) \\ x=80\text{\%} \end{gathered}`

c)

It is not possible to remove all the contaminants, due to the function nothing, since the moment that x is equal to 100, the denominator is 0, which causes a mathematical indeterminacy