Study question Im stuck on, (Curve sketching)

[Dave J]

Ok I have a test coming up and one of the questions in the review is the following.

Report the cost of cleaning up property. Cost can increase dramatically depending on percent of pollutants needed to be be removed. The cost C in dollars of removing p% of the pollutants from the site as C(p) = 50,000/(100-p)


There are 5 questions regarding it, I got em all fine but there is one that I am not sure about
2. Determine Lim x->100- C(p).

Could someone explain this to me, I am thinking its -Infinity, but I am not sure.

 

[Unco]

As p approaches 100 from the left, p is less than 100, so 100-p, and hence C(p), is positive or negative?

 

[skeeter]

as p gets close to 100%, the denominator of the function C(p) gets close to 0 ...
since the numerator stays fixed, you get a function that increases w/o bound.

Yes, the cost increases toward infinity ... in practical terms, this says that you can never achieve a 100% clean-up.