Applications using rational expressions and equations

[Gr8fu13]

1. The cost, in millions of dollars, to remove x % of pollution in a lake modeled by
c=6,000
200-2x
a. What is the cost to remove 75% of the pollutant?

b. What is the cost to remove 90% of the pollutant?

c. What is the cost to remove 99% of the pollutant?

d. For what value is this equation undefined?

e. Do the answers to sections a. through d. match your expectations? Explain why or why not.

I would think that for this I would just substitute the percentages for x. So for part a I would use .75 for x. I am not sure if I should simplify, factor, or what the next step would be. Can someone please help get me started on this? Thank you so much

 

[Gr8fu13]

Nevermind....I got it!

 

[tkhunny]

Too late.

\(\displaystyle c(x) = \frac{6000}{200-2x}\)

It looks like you're close. The definition is x%, so the % is already in there. To remove 75%, don't use 0.75, use 75. Always read your definitions VERY CAREFULLY. No factoring. Just evaluate.

d) Is probably a very bad question. I suspect it want's you to say x = 100, since that makes the denominator zero (0). However, this is a silly answer. Let's think about the Domain. In the business of removing polution, can we remove more than 100%? No. Can we remove less than 0%? No. Your function, c(x) is defined on [0,100) ONLY. It is UNdefiend for ANY value outside this Domain. Since I'm a smart aleck, I'd pick a weird value, just to get the chance to argue with the teacher in front of the class. Try x = 101. That will do it. Try x = -4. Better yet, try \(\displaystyle 48\pi\). I would laugh. On the other hand, your teacher may not have a sense of humor.