The original function is this: f(x)= 80p ÷ 100-x. (100-x is in the denominator.) The domain is all reals except 100. (more)

Question

The original function is this: f(x)= 80p ÷ 100-x. (100-x is in the denominator.) The domain is all reals except 100.  Here is what I need help with: The above equation is going to be tweaked to be C(p)= 80p ÷ 100-p. C(p) represents the cost (in thousands) to remove p percent of the pollutants from plant emissions from coal burning power plant. The domain is the same in both equations. Explain the significance of the domain when the equation has this new meaning. Include in the discussion what happens when p approaches the "domain exclusion number

Answer 1

The description is all about the meaning of the variables.

 

Because dividing by 0 is undefined, x may not be 100.  With the cost function, p may not be 100 (this means that you cannot remove 100% of the pollutants using this formula).

 

Now, when a denominator gets closer and closer to 0, the fraction gets humongous (I don't know any more emphatic word).  So, with a requirement of getting more and more and more (closer to 100%) of the pollutants out of the emissions, it is going to cost more and way more and "out of sight."

 

Now, it may be important to point out that x can be any real number except 100, but p has a range of 0≤p<100 (note: we must disallow 100% because we cannot have a 0 denominator).

 

The cost formula may have a practical or effective range based on actual data (full disclosure:  In the '80s, I managed computers at a DOE lab where they developed formulas to model Clean Coal processes so that we could shut down the old Gasifier and just run the computer model for days at a time).