91Ó°ÊÓ

A frozen yogurt stand makes a profit of \(P(x)=\) \(.40 x-80\) dollars when selling \(x\) scoops of yogurt per day. (a) Find the break-even sales level, that is, the level at which \(P(x)=0\). (b) What sales level generates a daily profit of $$\$ 30$$ ? (c) How many more scoops of yogurt will have to be sold to raise the daily profit from $$\$ 30$$ to $$\$ 40$$ ?

In Exercises \(21-28\), describe the domain of the function. $$ g(x)=\frac{1}{\sqrt{3-x}} $$

Compute the numbers. \(16^{-5}\)

A cellular telephone company estimates that, if it has \(x\) thousand subscribers, its monthly profit is \(P(x)\) thousand dollars, where \(P(x)=12 x-200\). (a) How many subscribers are needed for a monthly profit of 160 thousand dollars? (b) How many new subscribers would be needed to raise the monthly profit from 160 to 166 thousand dollars?

Cost of Cleaning a Pollutant Suppose that the cost (in millions of dollars) to remove \(x\) percent of a certain pollutant is given by the cost benefit function $$ f(x)=\frac{20 x}{102-x} \quad \text { for } 0 \leq x \leq 100 $$ (a) Find the cost to remove \(85 \%\) of the pollutant. (b) Find the cost to remove the final \(5 \%\) of the pollutant.

In Exercises \(21-28\), describe the domain of the function. $$ g(x)=\frac{4}{x(x+2)} $$

Let \(f(x)=\frac{x}{x-2}, g(x)=\frac{5-x}{5+x}\), and \(h(x)=\frac{x+1}{3 x-1}\). Express the following as rational functions. $$ h\left(\frac{1}{x^{2}}\right) $$

Each quadratic function in Exercises \(25-30\) has the form \(y=a x^{2}+b x+c\). Identify \(a, b\), and \(c\). $$ y=3 x^{2}-4 x $$

$$ \text { Factor the polynomials in Exercises } \text { . } $$ $$ x^{3}-1 $$

In Exercises \(21-28\), describe the domain of the function. $$ f(x)=\frac{3 x-5}{x^{2}+x-6} $$