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Chapter 2: Problem 20
Solve the inequality. Then graph the solution set. $$x^{2}+2 x>3$$
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Use Descartes's Rule of Signs to determine the possible numbers of positive and negative real zeros of the function. $$h(x)=2 x^{3}+3 x^{2}+1$$
Use the given zero to find all the zeros of the function. Function \(f(x)=x^{3}+4 x^{2}+14 x+20\) Zero \(-1-3 i\)
Think About It \(\quad\) Sketch the graph of a fifth-degree polynomial function whose leading coefficient is positive and that has a zero at \(x=3\) of multiplicity 2
Use Descartes's Rule of Signs to determine the possible numbers of positive and negative real zeros of the function. $$g(x)=2 x^{3}-3 x^{2}-3$$
The numbers \(N\) (in millions) of students enrolled in schools in the United States from 2000 through 2009 are shown in the table. $$\begin{array}{|c|c|}\hline \text { Year } & \text { Number, \(N\) } \\\\\hline 2000 & 72.2 \\\2001 & 73.1 \\\2002 & 74.0 \\\2003 & 74.9 \\\2004 & 75.5 \\\2005 & 75.8 \\\2006 & 75.2 \\\2007 & 76.0 \\\2008 & 76.3 \\\2009 & 77.3 \\\\\hline\end{array}$$ (a) Use a graphing utility to create a scatter plot of the data. Let \(t\) represent the year, with \(t=0\) corresponding to 2000. (b) Use the regression feature of the graphing utility to find a quartic model for the data. (A quartic model has the form \(a t^{4}+b t^{3}+c t^{2}+d t+e,\) where \(a, b\) \(c, d, \text { and } e \text { are constant and } t \text { is variable. })\) (c) Graph the model and the scatter plot in the same viewing window. How well does the model fit the data? (d) According to the model, when did the number of students enrolled in schools exceed 74 million? (e) Is the model valid for long-term predictions of student enrollment? Explain.
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