Chapter 1

The average hourly wage (adjusted to 1982 dollars) was \(\$ 7.66\) in 1990 and \(\$ 8.27\) in 2009 (Source: U.S. Census Bureau.) (a) Find a point-slope form of a line that passes through the points \((1990,7.66)\) and \((2009,8.27)\) (b) Interpret the slope. (c) Use the equation from part (a) to approximate the hourly wage in \(2005 .\) Compare it with the actual value of \(\$ 8.18\)

Solve each formula for the specified variable.} \(\mathrm{p}=a+b+c\) for \(c \quad\) (Perimeter of a triangle)

Find a decimal approximation of each root or power. Round answers to the nearest thousandth. $$23^{2.75}$$

Find \(f(a), f(b+1),\) and \(f(3 x)\) for the given \(f(x)\) $$f(x)=5 x$$

The table shows equivalent temperatures in degrees Celsius and degrees Fahrenheit. $$\begin{array}{c|c|c|c|c|c}\circ \mathrm{F} & -40 & 32 & 59 & 95 & 212 \\\\\hline^{\circ} \mathrm{C} & -40 & 0 & 15 & 35 & 100\end{array}$$ (a) Plot the data by having the \(x\) -axis correspond to Fahrenheit temperature and the \(y\) -axis to Celsius temperature. What type of relation exists between the data? (b) Find a function \(C\) that uses the Fahrenheit temperature \(x\) to calculate the corresponding Celsius temperature. Interpret the slope. (c) What is a temperature of \(83^{\circ} \mathrm{F}\) in degrees Celsius?

Solve each formula for the specified variable.} \(\mathscr{A}=\frac{1}{2} h\left(b_{1}+b_{2}\right)\) for \(h \quad\) (Area of a trapezoid)

Approximate each expression to the nearest hundredth. $$\frac{5.6-3.1}{8.9+1.3}$$

Find \(f(a), f(b+1),\) and \(f(3 x)\) for the given \(f(x)\) $$f(x)=x-5$$

Asian-American populations (in millions) are shown in the table. $$\begin{array}{|l|c|c|c|c|}\hline \text { Year } & 2003 & 2005 & 2007 & 2009 \\\\\hline \begin{array}{l}\text { Population } \\\\\text { (in millions) }\end{array} & 11.8 & 12.6 & 13.3 & 14.0\end{array}$$ (a) Use the points \((2003,11.8)\) and \((2009,14.0)\) to find the point-slope form of a line that models the data. \(\operatorname{Let}\left(x_{1}, y_{1}\right)=(2003,11.8)\) (b) Use this equation to estimate the Asian-American population in 2013 to the nearest tenth of a million.

Solve each formula for the specified variable.} \(\mathscr{A}=\frac{1}{2} h\left(b_{1}+b_{2}\right)\) for \(b_{2} \quad\) (Area of a trapezoid)

Approximate each expression to the nearest hundredth. $$\frac{34+25}{23}$$

Find \(f(a), f(b+1),\) and \(f(3 x)\) for the given \(f(x)\) $$f(x)=2 x-5$$

A linear function \(f\) has the ordered pairs listed in the table. Find the slope \(m\) of \(t F\) e table to find the \(y\) -intercept of the line, and give an equation that defines \(f\). \begin{array}{c|c} x & f(x) \\ \hline-3 & -10 \\ -2 & -6 \\ -1 & -2 \\ 0 & 2 \\ 1 & 6 \end{array}

The table lists the worldwide advertising revenue of Google (in billions of dollars). $$\begin{array}{|l|c|c|c|c|}\hline \text { Year } & 2005 & 2007 & 2009 & 2011 \\\\\hline \begin{array}{l}\text { Revenue } \\\\\text { (\$ billions) }\end{array} & 6 & 17 & 23 & 37 \\\\\hline\end{array}$$ (a) Find the point-slope form of the line that passes through the points \((2005,6)\) and \((2011,37) .\) Let \(\left(x_{1}, y_{1}\right)\) be \((2005,6)\) (b) Interpret the slope of the line. (c) Use this equation to estimate the revenue in 2007 and \(2009 .\) Compare these estimates with the actual values shown in the table.

Solve each formula for the specified variable.} \(S=2 L W+2 W H+2 H L\) for \(H \quad\) (Surface area of a rectangular box \()\)

Approximate each expression to the nearest hundredth. $$\sqrt{\pi^{3}+1}$$

Find \(f(a), f(b+1),\) and \(f(3 x)\) for the given \(f(x)\) $$f(x)=x^{2}$$

A linear function \(f\) has the ordered pairs listed in the table. Find the slope \(m\) of \(t F\) e table to find the \(y\) -intercept of the line, and give an equation that defines \(f\). \begin{array}{c|c} x & f(x) \\ \hline-3 & -10 \\ -2 & -6 \\ -1 & -2 \\ 0 & 2 \\ 1 & 6 \end{array}

The table lists U.S. print newspaper advertising revenue (in billions of dollars). $$\begin{array}{|l|c|c|c|c|}\hline \text { Year } & 2006 & 2008 & 2010 & 2012 \\\\\hline \begin{array}{l}\text { Revenue } \\\\\text { (\$billions) }\end{array} & 48 & 35 & 22 & 10 \\\\\hline\end{array}$$ (a) Find the point-slope form of the line that passes though \((2006,48)\) and \((2010,22) .\) Let \(\left(x_{1}, y_{1}\right)\) be \((2006,48)\) (b) Find the point-slope form of the line that passes though \((2008,35)\) and \((2012,10) .\) Let \(\left(x_{1}, y_{1}\right)\) be \((2008,35)\) (c) Interpret the slope of the line from part (b). (d) Use equations from parts (a) and (b) to predict the revenue for 2009

Solve each formula for the specified variable.} \(S=2 \pi r h+2 \pi r^{2}\) for \(h \quad\) (Surface area of a cylinder)

Approximate each expression to the nearest hundredth. $$\sqrt[3]{2.1-6^{2}}$$

Find \(f(a), f(b+1),\) and \(f(3 x)\) for the given \(f(x)\) $$f(x)=1-x^{2}$$

The table lists the average tuition and fees (in constant 2010 dollars) at private colleges and universities for selected years. $$\begin{array}{|l|c|c|c|c|}\hline \text { Year } & 1980 & 1990 & 2000 & 2010 \\\\\hline \begin{array}{l}\text { Tuition and Fees } \\\\\text { (in 2010 dollars) }\end{array} & 13,686 & 20,894 & 26,456 & 31,395 \\\\\hline\end{array}$$ (a) Find the equation of the least-squares regression line that models the data. (b) Graph the data and the regression line in the same viewing window. (c) Estimate tuition and fees in \(2005,\) and compare it with the actual value of \(\$ 29,307\).

Solve each formula for the specified variable.} \(V=\frac{1}{3} \pi r^{2} h\) for \(h \quad\) (Volume of a cone)

Approximate each expression to the nearest hundredth. $$3(5.9)^{2}-2(5.9)+6$$

Find \(f(a), f(b+1),\) and \(f(3 x)\) for the given \(f(x)\) $$f(x)=|x|+4$$

A linear function \(f\) has the ordered pairs listed in the table. Find the slope \(m\) of e table to find the \(y\) -intercept of the line, and give an equation that defines \(f\). begin{array}{rr|r} \text { 70. } & x & f(x) \\ \hline-100 & -4 \\ -50 & -4 \\ 0 & -4 \\ 50 & -4 \\ 100 & -4 \end{array}

The table lists the average tuition and fees (in constant 2010 dollars) at public colleges and universities for selected years. $$\begin{array}{|l|l|l|l|l|l|}\hline \text { Year } & 1980 & 1990 & 2000 & 2005 & 2010 \\\\\hline \begin{array}{l}\text { Tuition and Fees } \\\\\text { (in 2010 dollars) }\end{array} & 5938 & 7699 & 9390 & 11,386 & 13,297 \\\\\hline\end{array}$$ (a) Find the equation of the least-squares regression line that models the data. (b) Graph the data and the regression line in the same viewing window. (c) Estimate tuition and fees in 2007 . (d) Use the model to predict tuition and fees in 2016 .

Solve each formula for the specified variable.} \(y=a(x-h)^{2}+k\) for \(a\) (Mathematics)

Approximate each expression to the nearest hundredth. $$2 \pi^{3}-5 \pi^{2}-3$$

Work each problem. If \(f(-2)=3,\) identify a point on the graph of \(f\)

In the late \(1920 \mathrm{s}\), the famous observational astronomer Edwin P. Hubble ( \(1889-1953\) ) determined the distances to several galaxies and the velocities at which they were receding from Earth. Four galaxies with their distances in light-years and velocities in miles per second are listed in the table at the top of the next column. $$\begin{array}{|l|c|c|}\quad\quad\text { Galaxy } & \text { Distance } & \text { Velocity } \\\\\hline \text { Virgo } & 50 & 990 \\\\\text { Ursa Minor } & 650 & 9,300 \\\\\text { Corona Borealis } & 950 & 15,000 \\\\\text { Bootes } & 1,700 & 25,000\end{array}$$ (a) Let \(x\) represent velocity and \(y\) represent distance. Find the equation of the least-squares regression line that models the data. (b) If the galaxy Hydra is receding at a speed of \(37,000\) miles per second, estimate its distance from Earth.

Solve each formula for the specified variable.} $$S=\frac{n}{2}\left(a_{1}+a_{n}\right) \text { for } n \quad \text { (Mathematics) }$$

Approximate each expression to the nearest hundredth. $$\sqrt{(4-6)^{2}+(7+1)^{2}}$$

Work each problem. If \(f(3)=-9.7,\) identify a point on the graph of \(f .\)

The table lists the worldwide average household spending (in dollars) on Apple products for selected years. $$\begin{array}{|l|c|c|c|c|} \hline \text { Year } & 2009 & 2011 & 2013 & 2015 \\\ \hline \begin{array}{c} \text { Spending } \\ \text { (\$ dollars) } \end{array} & 62 & 158 & 265 & 444 \end{array}$$ (a) Use regression to find a formula \(f(x)=a x+b\) so that \(f\) models the data. (b) Interpret the slope of the graph of \(y=f(x)\) (c) Estimate the average household spending on Apple products in 2014 and compare it with the actual value of \(\$ 343\)

Solve each formula for the specified variable.} $$S=\frac{n}{2}\left[2 a_{1}+(n-1) d\right] \text { for } a_{1} \quad \text { (Mathematics) }$$

Approximate each expression to the nearest hundredth. $$\sqrt{[-1-(-3)]^{2}+(-5-3)^{2}}$$

Solve each formula for the specified variable.} \(s=\frac{1}{2} g t^{2}\) for \(g\) (Distance traveled by a falling object)

Approximate each expression to the nearest hundredth. $$\text { 73. } \frac{\sqrt{\pi-1}}{\sqrt{1+\pi}}$$

Work each problem. If the point \((-3,2)\) lies on the graph of \(f,\) then \(f(\quad)=\text {_____}\)

Solve each formula for the specified variable.} \(A=\frac{24 f}{B(p+1)}\) for \(p\) (Approximate annual interest rate)

Approximate each expression to the nearest hundredth. $$\sqrt[3]{4.5 \times 10^{5}+3.7 \times 10^{2}}$$

Sketch by hand the graph of the line passing through the given point and having the given slope. Label two points on the line. $$(-1,3), m=\frac{3}{2}$$

Investment problems such as those in Exercises \(75-80\) can be solved by using a method similar to the one explained in Example \(2,\) along with the simple- interest formula \(I=P R T\) where I is the interest earned, \(P\) is the initial amount of money deposited, \(R\) is the annual interest rate as a decimal, and \(T\) is the time the money is deposited in years. Solve each problem. Let \(T=1\) year for each exercise. Real-Estate Financing Cody Westmoreland wishes to sell a piece of property for \(\$ 240,000 .\) He wants the money to be paid off in two ways: a short-term note at \(6 \%\) interest and a long-term note at \(5 \% .\) Find the amount of each note if the total annual interest paid is \(\$ 13,000\).

Approximate each expression to the nearest hundredth. $$\frac{2}{1-\sqrt[3]{5}}$$

Sketch by hand the graph of the line passing through the given point and having the given slope. Label}\\\ &\text { two points on the line.} \end{aligned} \text { Through }(-2,8), m=-1

Investment problems such as those in Exercises \(75-80\) can be solved by using a method similar to the one explained in Example \(2,\) along with the simple- interest formula \(I=P R T\) where I is the interest earned, \(P\) is the initial amount of money deposited, \(R\) is the annual interest rate as a decimal, and \(T\) is the time the money is deposited in years. Solve each problem. Let \(T=1\) year for each exercise. Buying and Selling Land Bobby Aguillard bought two plots of land for a total of \(\$ 120,000 .\) When he sold the first plot, he made a profit of \(15 \% .\) When he sold the second, he lost \(10 \% .\) His total profit was \(\$ 5500 .\) How much did he pay for each piece of land?

In Exercises 75 and \(76,\) f and g are linear functions. If the solution set of \(f(x)

Approximate each expression to the nearest hundredth. $$1-\frac{4.5}{3-\sqrt{2}}$$