 2.2.5.1: Consider the equation . a. Find the value of A for n 5 0, 1, 20. b....
 2.2.6.1: Assuming m is the slope, identify the graph(s) where: a. m 5 3 b. c...
 2.2.7.1: Write an equation for the line through (22, 3) that has slope: a. 5...
 2.2.8.1: Using the general formula y mx that describes direct proportionalit...
 2.2.9.1: Construct the graphs of the following piecewise linear functions. B...
 2.2.1.1: If r is measured in inches, s in pounds, and t in minutes, identify...
 2.2.10.1: Match each equation with the appropriate table. a. y 5 3x 1 2 b. c....
 2.2.2.1: Calculate the average rate of change between adjacent points for th...
 2.2.3.1: Find the slope of a straight line that goes through: a. (5, 6) and ...
 2.2.11.1: The figures (top left of next page) show regression lines and corre...
 2.2.4.1: Examine the following graph of 30year fixed mortgage rates. Assumi...
 2.1: According to the National Association of Realtors, the median price...
 2.2.5.2: Consider the equation B 5 450 1 40n . a. Find the value of B for n ...
 2.2.6.2: Which line(s), if any, have a slope m such that: a. m k 5 2? b. m 5...
 2.2.7.2: Write an equation for the line through (0, 50) that has slope: a. 2...
 2.2.8.2: For each part, construct an equation and then use it to solve the p...
 2.2.9.2: Construct piecewise linear functions for the following graphs and d...
 2.2.1.2: Assume that R is measured in dollars, S in ounces, T in dollars per...
 2.2.10.2: Match each of the equations with the appropriate graph. a. y 5 10 2...
 2.2.2.2: Calculate the average rate of change between adjacent points for th...
 2.2.3.2: Find the slope of each line using the points where the graph inters...
 2.2.11.2: The accompanying graph and regression line show median personal tot...
 2.2.4.2: Compare the accompanying graphs. a. Which line appears to have the ...
 2.2: a. According to Apple Computer, sales of its iPod (the worlds best...
 2.2.5.3: Determine if any of the following points satisfy one or both of the...
 2.2.6.3: For each set of conditions, construct a linear equation and draw it...
 2.2.7.3: Calculate the slope and write an equation for the linear function r...
 2.2.8.3: In the accompanying table y is directly proportional to x. x 5 1 4 ...
 2.2.9.3: Given the following graph of g(x) on the next page: a. Construct a ...
 2.2.1.3: Your cars gas tank is full and you take a trip. You travel 212 mile...
 2.2.10.3: (Graphing program recommended.) Identify which of the following dat...
 2.2.2.3: The accompanying table shows the number of registered motor vehicle...
 2.2.3.3: Find the slope of each line using the points where the line crosses...
 2.2.11.3: The following equation represents the bestfit regression line for ...
 2.2.4.3: Compare the accompanying graphs. a. Which line appears to have the ...
 2.3: Given the following graph of the function h(t), identify any interv...
 2.2.5.4: Suppose during a 5year period the profit P(Y ) (in billions of dol...
 2.2.6.4: Construct a linear equation for each of the following conditions. a...
 2.2.7.4: Determine which of the following tables represents a linear functio...
 2.2.8.4: The electrical resistance R (in ohms) of a wire is directly proport...
 2.2.9.4: a. Normal human body temperature is often cited as 98.6 F. However,...
 2.2.1.4: The gas gauge on your car is broken, but you know that the car aver...
 2.2.10.4: (Graphing program recommended.) Plot the data in each of the follow...
 2.2.2.4: (Graphing program optional.) The accompanying table indicates the n...
 2.2.3.4: Examine the line segments A, B, and C. a. Which line segment has a ...
 2.2.11.4: The following equation represents a bestfit regression line for me...
 2.2.4.4: The following graphs show the same function graphed on different sc...
 2.4: Which line has the steeper slope? Explain why.
 2.5: You are traveling abroad and realize that American, British, and Fr...
 2.2.5.5: Consider the equation D 5 3.40 1 0.11n a. Find the values of D for ...
 2.2.6.5: Match the graph with the correct equation. a. y 5 x b. y 5 2x c. d....
 2.2.7.5: Plot each pair of points, then determine the equation of the line t...
 2.2.8.5: For each of the following linear functions, determine the independe...
 2.2.9.5: Assume two individuals, A and B, are traveling by car and initially...
 2.2.1.5: The consumption of margarine (in pounds per person) decreased from ...
 2.2.10.5: Determine which data represent exactly linear and which approximate...
 2.2.2.5: Calculate the average rate of change between adjacent points for th...
 2.2.3.5: Given the following graph: a. Estimate the slope for each line segm...
 2.2.11.5: From the FAM1000 data, the bestfit regression line for median pers...
 2.2.4.5: The following graph shows the National Assessment of Educational Pr...
 2.2.4.6: Generate two graphs and on each draw a line through the points (0, ...
 2.6: A bathtub that initially holds 50 gallons of water starts draining ...
 2.2.5.6: Suppose the equations and G(n) 5 12,000 1 800n give the total cost ...
 2.2.6.6: Match the function with its graph. (Note: There is one graph that h...
 2.2.7.6: Find the equation for each of the lines AC on the accompanying graph.
 2.2.8.6: On the scale of a map 1 inch represents a distance of 35 miles. a. ...
 2.2.9.6: On Christmas Day 2009, there was a bomb scare aboard a Detroitboun...
 2.2.1.6: The percentage of people who own homes in the United States has gon...
 2.2.10.6: In 2002 the United States consumed 617 million gallons of wine and ...
 2.2.2.6: Calculate the average rate of change between adjacent points for ea...
 2.2.3.6: Plot each pair of points and calculate the slope of the line that p...
 2.2.11.6: We can look for correlations for personal earnings with other varia...
 2.2.4.7: a. Generate a graph of a line through the points (0, 2) and (5, 2)....
 2.7: Cell phones have produced a seismic cultural shift. No other recent...
 2.2.5.7: If the equation gives the total cost of heating/cooling a home afte...
 2.2.6.7: In each part construct three different linear equations that all ha...
 2.2.7.7: Put the following equations in y b mx form, then identify the slope...
 2.2.8.7: Find a function that represents the relationship between distance, ...
 2.2.9.7: The greatest integer function y [x] is defined as the greatest inte...
 2.2.1.7: The accompanying table shows females SAT scores in 2000 and 2008. F...
 2.2.10.7: The percentage of medical degrees awarded to women in the United St...
 2.2.2.7: Each of the following functions has a graph that is increasing. If ...
 2.2.3.7: The following problems represent calculations of the slopes of diff...
 2.2.11.7: The term linear regression was coined in 1903 by Karl Pearson as pa...
 2.2.4.8: What are three adjectives (like explosive) that would imply rapid g...
 2.8: The following graph shows average salaries for major league basebal...
 2.2.5.8: Over a 5month period at Acadia National Park in Maine, the mean ni...
 2.2.6.8: Which equation has the steepest slope? a. y 5 2 2 7x b. y 5 2x 1 7 ...
 2.2.7.8: (Graphing program optional.) Solve each equation for y in terms of ...
 2.2.8.8: Determine which (if any) of the following variables (w, y, or z) is...
 2.2.9.8: The following table shows U.S. firstclass stamp prices (per ounce)...
 2.2.1.8: a. In 1992 the aerospace industry showed a net loss (negative profi...
 2.2.10.8: The accompanying graph shows the mortality rates (in deaths per 100...
 2.2.2.8: Match each data table with its graph.
 2.2.3.8: Find the slope m of the line through the points (0, b) and (x, y), ...
 2.2.11.8: The book Performing ArtsThe Economic Dilemma studied the economics ...
 2.2.4.9: What are three adjectives (like severe) that would imply rapid decl...
 2.9: Match one or more of the following graphs with the following descri...
 2.2.5.9: A residential customer in the Midwest purchases gas from a utility ...
 2.2.6.9: Given the function Q(t) 5 13 2 5t, construct a related function who...
 2.2.7.9: Complete the table for each of the linear functions, and then sketc...
 2.2.8.9: Find the slope of the line through the pair of points, then determi...
 2.2.9.9: Sketch a graph for each of the following situations. a. The amount ...
 2.2.1.9: The U.S. Bureau of the Census provided the following data concernin...
 2.2.10.9: The accompanying scatter plot shows the relationship between litera...
 2.2.2.9: Refer to the first two data tables (A and B) in Exercise 8. Insert ...
 2.2.3.9: Find the value of t if m is the slope of the line that passes throu...
 2.2.11.9: (Optional use of technology.) The graph at the top of the next page...
 2.2.4.10: (Graphing program optional.) Examine the data given on women in the...
 2.10: a. If you travel to China, the exchange rate at the Beijing airport...
 2.2.5.10: Create the formula for converting degrees centigrade, C, to degrees...
 2.2.6.10: Given the equation C(n) 5 30 1 15n, construct a related equation wh...
 2.2.7.10: (Graphing program optional.) The equation K 5 4F 2 160 models the r...
 2.2.8.10: Describe the graphs of the following equations. a. y 5 22 c. e. y 5...
 2.2.9.10: A department store is offering a coupon for 20% off for any purchas...
 2.2.1.10: According to the U.S. Bureau of the Census, the percentage of perso...
 2.2.10.10: The accompanying graph shows data for the mens Olympic 16pound sho...
 2.2.2.10: Following are data on the U.S. population over the time period 1830...
 2.2.3.10: a. Find the value of x so that the slope of the line through (x, 5)...
 2.2.11.10: Stroke is the thirdleading cause of death in the United States, be...
 2.2.4.11: On the following page there is a graph on AIDS in America similar t...
 2.11: In May 2010 the Gallup poll reported that 46% of Americans said tha...
 2.2.5.11: Determine the vertical intercept and the rate of change for each of...
 2.2.6.11: On the same grid, graph (and label with the correct equation) three...
 2.2.7.11: Find an equation to represent the cost of attending college classes...
 2.2.8.11: The accompanying figure shows the quantity of books (in millions) s...
 2.2.9.11: A namebrand cookie mix calls for baking cookies at a temperature o...
 2.2.1.11: According to a 2010 Kaiser Family Foundation report, during 2009 ki...
 2.2.10.11: Cell phones have become immensely popular, as the following chart s...
 2.2.2.11: (Technology recommended.) The accompanying data give a picture of t...
 2.2.3.11: Points that lie on the same straight line are said to be collinear....
 2.2.11.11: (Requires technology.) In Section 2.10 we examined the percentage o...
 2.2.4.12: (Course software required.) Open L6: Changing Axis Scales in Linear...
 2.12: Given the following graph: a. Find the equations of line A and line...
 2.2.5.12: 12. A hiker can walk 2 miles in 45 minutes. a. What is his average ...
 2.2.6.12: On the same grid, graph (and label with the correct equation) three...
 2.2.7.12: a. Write an equation that describes the total cost to produce x ite...
 2.2.8.12: An employee for an aeronautical corporation had a starting salary o...
 2.2.9.12: a. Create a piecewise function and sketch the graph of the followin...
 2.2.1.12: The following graph was produced by the U.S. Department of Transpor...
 2.2.10.12: The accompanying graph shows the relationship between the age of a ...
 2.2.3.12: a. Find the slope of the line through each of the following pairs o...
 2.2.11.12: (Requires technology.) The accompanying table shows the calories pe...
 2.2.4.13: The accompanying graphs show the same data on the median income of ...
 2.13: According to the Environmental Protection Agencys National Coastal ...
 2.2.5.13: The cost C(x) of producing x items is determined by adding fixed co...
 2.2.6.13: Given the following graphs of three straight lines: a. Which has th...
 2.2.7.13: Your bank charges you a $2.50 monthly maintenance fee on your check...
 2.2.8.13: For each of the given points write equations for three lines that a...
 2.2.9.13: Create a piecewise linear function and sketch a graph for this scen...
 2.2.1.13: Use the information in the accompanying table to answer the followi...
 2.2.10.13: (Graphing program recommended.) The data in the table below show th...
 2.2.3.13: Graph a line through each pair of points and then calculate its slo...
 2.2.11.13: (Optional use of technology.) The accompanying graph shows the winn...
 2.2.4.14: The accompanying graph shows the number of Nobel Prizes awarded in ...
 2.14: Generate the equation for a line under each of the following condit...
 2.2.5.14: A new $25,000 car depreciates in value by $5000 per year. Construct...
 2.2.7.14: If a town starts with a population of 63,500 that declines by 700 p...
 2.2.8.14: Consider the function (x) 4. a. What is (0)? (30)? (12.6)? b. Descr...
 2.2.9.14: To motivate customers, Puget Sound Energy explored ways to set lowe...
 2.2.1.14: The data show U.S. consumption and exports of cigarettes. a. Calcul...
 2.2.10.14: Hybrid car sales peaked in early 2008, then showed a steady decline...
 2.2.3.14: Find some possible values of the ycoordinates for the points (3, y...
 2.2.11.14: (Optional use of technology.) The accompanying graph shows the worl...
 2.2.4.15: The following graph shows the trend in National Assessment of Educa...
 2.15: In 2005 a record 51.5% of paper consumed in the United States (51.3...
 2.2.5.15: The state of Pennsylvania has a 6% sales tax on taxable items. (Not...
 2.2.7.15: A teachers union has negotiated a uniform salary increase for each ...
 2.2.8.15: A football player who weighs 175 pounds is instructed at the end of...
 2.2.9.15: Interval training is a series of repetitions of work with a recover...
 2.2.1.15: Examine the accompanying table on life expectancy. a. What group ha...
 2.2.10.15: (Graphing program recommended.) The Gas Guzzler Tax is imposed on m...
 2.2.3.15: Calculate the slope of the line passing through each of the followi...
 2.2.11.15: The temperature at which water boils is affected by the difference ...
 2.16: Sketch a graph that could represent each of the following situation...
 2.2.5.16: a. If S(x) 5 20,000 1 1000x describes the annual salary in dollars ...
 2.2.7.16: Your favorite aunt put money in a savings account for you. The acco...
 2.2.8.16: . a. Write an equation for the line parallel to y 2 4x that passes ...
 2.2.9.16: . A 60yearold U.S. Masters swimmer swam a 200yard freestyle in 2...
 2.2.1.16: The table below shows U.S. marital status a. Calculate the average ...
 2.2.10.16: A veterinarians office displayed the following table comparing dog ...
 2.2.3.16: Which pairs of points produce a line with a negative slope? a. (5, ...
 2.2.11.16: (Optional use of technology.) The accompanying graph shows the worl...
 2.17: Generate an equation for each line A, B, C, D, and E shown in the a...
 2.2.5.17: The following represent linear equations written using only units o...
 2.2.7.17: You read in the newspaper that the river is polluted with 285 parts...
 2.2.8.17: a. Write an equation for the line parallel to y 4 x that passes thr...
 2.2.10.17: In general, heavier cars get lower or worse gas mileage than lighte...
 2.2.3.17: In the previous exercise, which pairs of points produce a line with...
 2.2.11.17: (Optional use of technology.) The accompanying graph shows the incr...
 2.18: U.S. life expectancy has been steadily increasing (see Exercise 15 ...
 2.2.5.18: 18. Identify the slopes and the vertical intercepts of the lines wi...
 2.2.7.18: The womens recommended weight formula from Harvard Pilgrim Healthca...
 2.2.8.18: Construct the equation of a line that goes through the origin and i...
 2.2.10.18: The following scatter plot shows the relationship between the avera...
 2.2.3.18: A study on numerous streams examined the effects of a warming clima...
 2.2.11.18: (Requires technology.) Examine the following data on U.S. union mem...
 2.19: For the function g(x) 5 uxu 1 2: a. Generate a table of values for ...
 2.2.5.19: For each of the following, find the slope and the vertical intercep...
 2.2.7.19: In 1977 a math professor bought her condominium in Cambridge, Massa...
 2.2.8.19: Construct the equation of a line that goes through the origin and i...
 2.2.3.19: Handicapped Vietnam veterans successfully lobbied for improvements ...
 2.2.11.19: If a study shows that smoking and lung cancer have a high positive ...
 2.20: In Exercise 7 in Section 2.9 we met the greatest integer function f...
 2.2.5.20: Construct an equation and sketch the graph of its line with the giv...
 2.2.7.20: The yaxis, the xaxis, the line x 5 6, and the line y 5 12 determi...
 2.2.8.20: Which lines are parallel to each other? Which lines are perpendicul...
 2.2.3.20: The following graph shows the relationship between education and he...
 2.2.11.20: Parental income has been found to have a high positive correlation ...
 2.21: The table below gives historical data on voter turnout as a percent...
 2.2.5.21: In Exercises 21 to 23 find an equation, generate a small table of s...
 2.2.7.21: . Find the equation of the line shown on the accompanying graph. Us...
 2.2.8.21: Because different scales may be used on the horizontal and vertical...
 2.2.3.21: Read the Anthology article Slopes on the course website and then de...
 2.22: a. Construct the equation of a line y1 whose graph is steeper than ...
 2.2.5.22: In Exercises 21 to 23 find an equation, generate a small table of s...
 2.2.7.22: You are living in Paris but will be traveling in London. The exchan...
 2.2.8.22: In each part construct the equations of two lines that: a. Are para...
 2.23: Sweden has kept meticulous records of its population for many years...
 2.2.5.23: In Exercises 21 to 23 find an equation, generate a small table of s...
 2.2.7.23: According to Moodys www.econ.com. in the fourth quarter of 2006, 6....
 2.2.8.23: For each of the accompanying graphs you dont need to do any calcula...
 2.24: According to the U.S. Environmental Protection Agency, carbon dioxi...
 2.2.5.24: Estimate b (the yintercept) and m (the slope) for each of the acco...
 2.2.7.24: a. Create a third column in Tables A and B, and insert values for t...
 2.2.8.24: Find the equation of the line in the form y mx b for each of the fo...
 2.25: The following three graphs show U.S. farm income for three crops ov...
 2.2.7.25: Adding minerals or organic compounds to water lowers its freezing p...
 2.2.8.25: In the equation Ax By C: a. Solve for y so as to rewrite the equati...
 2.26: The World Health Organization (WHO) states: Access to drinking wate...
 2.2.7.26: The accompanying data show rounded mean values for blood alcohol co...
 2.2.8.26: Use the results of Exercise 25, parts (c) and (d), to find the slop...
 2.27: If f(x) 5 y is decreasing throughout, then the y values decrease as...
 2.28: Having a slope of zero is the same as having an undefined slope.
 2.29: A vertical line can be described by a linear function.
 2.30: Two nonvertical lines that are perpendicular must have slopes of op...
 2.31: . All linear functions can be written in the form y 5 b 1 mx
 2.32: In 3241, give an example of a function or functions with the specif...
 2.33: In 3241, give an example of a function or functions with the specif...
 2.34: In 3241, give an example of a function or functions with the specif...
 2.35: In 3241, give an example of a function or functions with the specif...
 2.36: In 3241, give an example of a function or functions with the specif...
 2.37: In 3241, give an example of a function or functions with the specif...
 2.38: In 3241, give an example of a function or functions with the specif...
 2.39: In 3241, give an example of a function or functions with the specif...
 2.40: In 3241, give an example of a function or functions with the specif...
 2.41: In 3241, give an example of a function or functions with the specif...
 2.42: Is each of the statements in 4255 true or false? If a statement is ...
 2.43: Is each of the statements in 4255 true or false? If a statement is ...
 2.44: Is each of the statements in 4255 true or false? If a statement is ...
 2.45: Is each of the statements in 4255 true or false? If a statement is ...
 2.46: Is each of the statements in 4255 true or false? If a statement is ...
 2.47: Is each of the statements in 4255 true or false? If a statement is ...
 2.48: Is each of the statements in 4255 true or false? If a statement is ...
 2.49: Is each of the statements in 4255 true or false? If a statement is ...
 2.50: Is each of the statements in 4255 true or false? If a statement is ...
 2.51: Is each of the statements in 4255 true or false? If a statement is ...
 2.52: Is each of the statements in 4255 true or false? If a statement is ...
 2.53: Is each of the statements in 4255 true or false? If a statement is ...
 2.54: Is each of the statements in 4255 true or false? If a statement is ...
 2.55: Is each of the statements in 4255 true or false? If a statement is ...
Solutions for Chapter 2: RATES OF CHANGE AND LINEAR FUNCTIONS
Full solutions for Explorations in College Algebra  5th Edition
ISBN: 9780470466445
Solutions for Chapter 2: RATES OF CHANGE AND LINEAR FUNCTIONS
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 261 problems in chapter 2: RATES OF CHANGE AND LINEAR FUNCTIONS have been answered, more than 10438 students have viewed full stepbystep solutions from this chapter. Chapter 2: RATES OF CHANGE AND LINEAR FUNCTIONS includes 261 full stepbystep solutions. This textbook survival guide was created for the textbook: Explorations in College Algebra, edition: 5. Explorations in College Algebra was written by and is associated to the ISBN: 9780470466445.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Iterative method.
A sequence of steps intended to approach the desired solution.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.