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Chapter 0: Problem 128
Think About It Is it possible for two lines with positive slopes to be perpendicular? Explain.
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College Students The numbers of foreign students \(F\) (in thousands) enrolled in colleges in the United States from 1992 to 2002 can be approximated by the model. $$ F=0.004 t^{4}+0.46 t^{2}+431.6, \quad 2 \leq t \leq 12 $$ where \(t\) represents the year, with \(t=2\) corresponding to 1992. (Source: Institute of International Education) (a) Use a graphing utility to graph the model. (b) Find the average rate of change of the model from 1992 to 2002. Interpret your answer in the context of the problem. (c) Find the five-year time periods when the rate of change was the greatest and the least.
Determine whether the function is even, odd, or neither. Then describe the symmetry. $$ f(t)=t^{2}+2 t-3 $$
True or False? In Exercises 85 and 86, determine whether the statement is true or false. Justify your answer. $$ \text { If } f \text { is an even function, } f^{-1} \text { exists. } $$
In Exercises 27 and 28, use the table of values for \(y=f(x)\) to complete a table for \(y=f^{-1}(x)\). $$ \begin{array}{|l|r|r|r|r|r|r|} \hline x & -3 & -2 & -1 & 0 & 1 & 2 \\ \hline f(x) & -10 & -7 & -4 & -1 & 2 & 5 \\ \hline \end{array} $$
(a) use the position equation \(s=-16 t^{2}+v_{0} t+s_{0}\) to write a function that represents the situation, (b) use a graphing utility to graph the function, (c) find the average rate of change of the function from \(t_{1}\) to \(t_{2}\), (d) interpret your answer to part (c) in the context of the problem, (e) find the equation of the secant line through \(t_{1}\) and \(t_{2}\), and (f) graph the secant line in the same viewing window as your position function. An object is thrown upward from ground level at a velocity of 120 feet per second. $$ t_{1}=3, t_{2}=5 $$
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