Chapter 4.4, Problem 81E

Pollution. In Silicon Valley, a number of computer firms were found to be contaminating underground water supplies with toxic chemicals stored in leaking underground containers. A water quality control agency ordered the companies to take immediate corrective action and contribute to a monetary pool for the testing and cleanup of the underground contamination. Suppose that the required monetary pool (in millions of dollars) is given by

     $P\left(x\right)=\frac{2x}{1-x}0\le x<1$

where x is the percentage (expressed as a decimal fraction) of the total contaminant removed.

1. (A) Where is P(x) increasing? Decreasing?
2. (B) Where is the graph of P concave upward? Downward?
3. (C) Find any horizontal or vertical asymptotes.
4. (D) Find the x and y intercepts.
5. (E) Sketch a graph of P.