0

I have found this function in several math textbooks:

$$ C(p)=\frac{80000p}{100-p} $$

It represents the cost C(p) to remove the percent p of impurities from coal. The function shows that as we try to remove a higher percentage of impurities, the cost goes up faster and faster, and it is impossible (mathematically, anyway) to remove 100% of the impurities because we approach infinity there--we have an asymptote.

I am trying to understand what this expression

$$ \frac{p}{100-p} $$

represents.

When p is 1, it's 1/99. When p is 50, it's 1, when p is 99 it's 99. I have found this expression in a few other models. Is there a name for it? What is it doing?

user3050028
  • 49
  • 2
  • It is the ratio of impurities removed to impurities remaining. It is similar to an odds ratio calculated from a probability, and its logarithm is similar to the logit function – Henry Apr 13 '20 at 17:20
  • Thank you. I know this is "percent removed" over "percent remaining," but what does that number represent in this problem? I am having trouble imagining what the number one obtains by taking "odds" would be used for. One uses the probability to calculate expected values and things like that. What does one use "odds" to calculate? – user3050028 Apr 13 '20 at 19:53

0 Answers0