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Chapter 3: Problem 114
Rewrite \(4-5 x-x^{2}+6 x^{3}\) in descending powers of \(x\).
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A mong all deaths from a particular disease, the percentage that is smoking related \((21-39\) cigarethes per day) is a function of the discase's incidence ratio. The incidence ratio describes the number of times more likely smokers are than nonsmokers to die from the disease. The following table shows the incidence ratios for heart disease and lung cancer for two age groups. For example, the incidence ratio of 9 in the table means that smokers befween the ages of 65 and 74 are 9 times more likely than nonsmokers in the same age group to die from lung cancer. The rational function$$ P(x)=\frac{100(x-1)}{x} $$models the percentage of smoking-related deaths among all deaths from a disease, \(P(x),\) in terms of the disease's incidence ratio, \(x\). The graph of the rational function is shown. What is the horizontal asymptote of the graph? Describe what this means about the percentage of deaths caused by smoking with increasing incidence ratios.
Use a graphing utility to graph \(y=\frac{1}{x^{\prime}}, y=\frac{1}{x^{3}},\) and \(\frac{1}{x^{5}}\) in the same viewing rectangle. For odd values of \(n,\) how does changing \(n\) affect the graph of \(y=\frac{1}{x^{n}} ?\)
Basic Car Rental charges \(\$ 20\) a day plus \(\$ 0.10\) per mile, whereas Acme Car Rental charges \(\$ 30\) a day plus \(\$ 0.05\) per mile. How many miles must be driven to make the daily cost of a Basic Rental a better deal than an Acme Rental? (Section 1.7, Example 11)
In Exercises 104鈥�107, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. There is more than one third-degree polynomial function with the same three \(x\) -intercepts.
In Exercises 100鈥�103, determine whether each statement makes sense or does not make sense, and explain your reasoning. I'm graphing a fourth-degree polynomial function with four turning points.
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