Statistics Solutions

(Solution Library) POLLUTION CONTROL A large city commissions a study that indicates that spending money on pollution control is effective up to a point

Question: POLLUTION CONTROL A large city commissions a study that indicates that spending money on pollution control is effective up to a point but eventually becomes wasteful. Suppose it is known that when \(x\) million dollars is spent on controlling pollution, the percentage of pollution removed is given by

\[P(x)=\frac{100 \sqrt{x}}{0.03 x^{2}+9}\]
  1. At what rate is the percentage of pollution removal \(P(x)\) changing when 16 million dollars are spent? Is the percentage increasing or decreasing at this level of expenditure?
  2. For what values of \(x\) is \(P(x)\) increasing? For what values of \(x\) is \(P(x)\) decreasing?

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