Appendix E. Fueling Up. Application Practice

Transcription

1 Appendix E Fueling Up Motorists often complain about rising gas prices. Some motorists purchase fuel efficient vehicles and participate in trip reduction plans, such as carpooling and using alternative transportation. Other drivers try to drive only when necessary. Application Practice Answer the following questions. Use Equation Editor to write mathematical expressions and equations. First, save this file to your hard drive by selecting Save As from the File menu. Click the white space below each question to maintain proper formatting. 1. Suppose you are at the gas station filling your tank with gas. The function C(g) represents the cost C of filling up the gas tank with g gallons. Given the equation: C(g) = 3.03(g) a) What does the number 3.03 represent? b) Find C(2) c) Find C(9) d) For the average motorist, name one value for g that would be inappropriate for this function's purpose. Explain why you chose the number you did. e) If you were to graph C(g), what would be an appropriate domain? Range? Explain your reasoning. 2. Examine the rise in gasoline prices from 1997 to The price of regular unleaded gasoline in January 1997 was $1.26 and in January 2006 the price of regular unleaded gasoline was $2.31 (Bureau of Labor Statistics, 2006). Use the coordinates (1997, 1.26) and (2006, 2.31) to find the slope (or rate of change) between the two points. Describe how you arrived at your answer. 3. The linear equation represents an estimate of the average cost of gas for year x starting in The year 1997 would be represented by x = 1, for example, as it is the first year in the study. Similarly, 2005 would be year 9, or X= 9. a) What year would be represented by x = 4? b) What x-value represents the year 2018? c) What is the slope (or rate of change) of this equation? d) What is the y-intercept? MAT 116

2 e) What does the y-intercept represent? f) Assuming this growth trend continues, what will the price of gasoline be in the year How did you arrive at your answer? 4. The line represents an estimate of the average cost of gasoline for each year. The line 0.1 1~ - y = estimates the price of gasoline in January of each year (Bureau of Labor Statistics, 2006). a) Do you expect the lines to be intersecting, parallel, or perpendicular? Explain your reasoning. b) Use the equations of the lines to determine if they are parallel. What did you find? c) Did your answer to part b confirm your expectation in part a? References Bureau of Labor Statistics (2006). Consumer price index. Retrieved June 1, 2007 from bls.govlcgi-binlsurveymost?ap. MAT 116

3 ~. 1. Find the slope and the y-intercept. The slope is. The y-intercept is ( Find the slope and the y-intercept of the line. Write the fractional answer in lowest tenns. The slope is U. (Type an integer or a fraction.) The y-intercept is ( 00. (Type an integer or a fraction.) 3. Find the slope and the y-intercept. The slope is 0. (Type an integer or a decimal.) The y-intercept is ( 00. (Type an integer or a decimal.) 4. Find the slope and the y-intercept of the line. The slope is u. (Type an integer or a fraction.) The y-intercept is (0, D. (Type an integer or a fraction.) ~

4 5. Find the slope and the y-intercept. The slope is. The y-intercept is (0,O), 6. Find the slope and the y-intercept of the line. Write fractional answers in lowest terms. The slope is U. The y-intercept is (0,u). 7. Find the slope of the line. The slope of the line is m =. (Simplify your answer. Type an integer or a fraction. Type N if the slope is undefined.) I " " " I " I X 8. Find the slope of the line. The slope of the line is m =. (Type an integer or a simplified fraction. Type N if the slope is undefined.)

5 - - Find. the slope, if it i exists, of the line m The slope rn =. (Simplify your answer. Type an integer or a fraction. Type N if the slope is undefined.) 10. Find the slope, if it exists, of the line containing the pair of points. he slope m = U. (Simplify your answer. Type an integer or a fraction. Type N if the slope is undefined.) (thousands of dollars) S Value Find the rate of change. The rate of change is thousand dollars day of Usc For the graph, find the average rate of change as a reduced fraction. Also, state the appropriate units (do not abbreviate). The rate of change is U. (Do not enter the units.) The appropriate units are pages per. Pages Days o,,, m m m,,,,,, 0 10 Page 3

6 13. Use the intercepts to graph the equation. lay x-2=y Use the graphing tool to graph the line. Use the 4- intercepts when drawing the line. If only one 2- intercept exists, use it and another point to draw the line x r s ~ s ~ E ~ l ~ o r ~ u ~ ~ Find the intercepts and then use them to graph the equation. Use the graphing tool to graph the line. Use the intercepts when drawing the line. If only one intercept exists, use it and another point to draw the line.

7 Find the intercepts and then use them to graph the sfy equation. Use the graphing tool to graph the line. Use the i 1 intercepts when-drawing the line. If only one intercept exists, use it and another point to draw -k -b -i -\-, the line. : I x I I I I I * Graph the equation using the slope and the y-intercept. Use the graphing tool to graph the line. Use the slope and y-intercept when drawing the line. I ~ I ~ I ~ 4 I ~ I ~ ilck to '' X l ~ g ~ Q ~ n ~ l ~ * Page 5

8 17. Graph using the slope and the y-intercept. loty Use the graphing tool to graph the line. Use the slope a and " y-intercept.. when drawing the line.. (@ :E: J 18. Graph the equation by plotting points. Use the graphing tool on the right to graph the equation. Cllck to Page 6

9 - Graph the equation by plotting points. losy y= -2 Use the graphing tool on the right to graph the equation. Click to 20. Determine whether the graphs of the pair of lines are parallel. What is the slope of the line x + 8 = y? (Type N if the slope is undefined.) What is the slope of the line y - x = - 4? (Type N if the slope is undefined.) Are the graphs of the given equations parallel? 0 No 0 Yes

10 2 1. Determine whether the graphs of each pair of lines are parallel. Are the graphs of the given equations parallel? 0 Yes 0 No 22. Determine whether the graphs of the two equations are perpendicular. Are the graphs of the given equations perpendicular? 0 No 0 Yes 23. Determine whether the graphs of the equations are perpendicular. Are the graphs of the given equations perpendicular? 0 No 0 Yes 24. Find the slope-intercept equation of the line that has the given characteristics. Slope 4 and y-intercept (0,9) The slope-intercept equation is y =. 25. Find the slope-intercept equation of the line that has the given characteristics. Slope 8.4 and y-intercept (0, - 4) The slope-intercept equation y =. (Use integers or decimals for any numbers in the expression.)

11 Find an equation of the line having the given slope and containing the given point. m = 4, (7,2) The equation of the line in slope-intercept form is y =. (Simplifjl your answer. Use integers or fractions for any numbers in the expression.) 27. Find an equation of the line having the given slope and containing the given point. The equation of the line is y =. (Simplifjl your answer. Use integers or fractions for any numbers in the expression.) 28. Find an equation of the line containing the given pair of points. Express your answer in the fonn x=a,y=b,ory=rnx+b. ( - 9, - 9) and (7,7) What is an equation of the line? Y'O (Use integers or fractions for any numbers in the expression.) 29. Find an equation of the line containing the given pair of points. (-3,-@and(-8,-9) The equation of the line in slope-intercept form is y = 0. (Simplify your answer. Use integers or fractions for any numbers in the expression.) 30. Find an equation of the line containing the given pair of points. (i, - +) and ($3) What is the equation of the line? Y '0 - - (SirnplifL your answer. Type answer in the form y = rnx + b using integers or fractions.) Page 9

12 3 1. Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y = rnx + b. The quation of the line is y = 0. (Simplif'y your answer. Use integers or tiactions for any numbers in the expression.) 32. Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y = mx +b. The equation of the line is y = (Simplify your answer. Use integers or fractions for any numbers in the expression.) 33. Write an equation of the line containing the given point and perpendicular to the given line. Express your answer in the form y = mx +b. (5,9); 4x +y -6 The equation of the line is y =. (Simplify your answer. Use integers or fractions for any numbers in the expression.) 34. Write an equation of the line containing the given point and perpendicular to the given line. The equation of the line is y =. (Type your answer in the fom y = mx +b. Simplify your answer. Type an integer or a fraction.)

13 35. Media Services charges $40 for a phone and Choose the correct graph of C(t). $2Olmonth for its economy plan. OA. OB. Find a model that determines the total cost, C(t), of operating a Media Services phone for t months. at) > Cft) = Use the model to find the total cost for 5 months of service. 0 C. OD. Total cost = $0 36. The table lists data regarding the average salaries of Year Average Salary several professional athletes in the years 1991 and $269,000 a) Use the c@ta points to find a linear function that fits the 2001 $1,440,000 data. b) Use the function to predict the average salary in 2005 and A linear hction that fits the data is S(x) = 0. (Let x = the number of years since 1990, and let S = the average salary x years from 1990.) The predicted average saw for 2005 is $0. (Round to the nearest whole number.) The predicted svarage salary for is $. (Round to the nearest whole number.) Page 11

14 37. In 1920, the record for a certain race was 46.4 sec. In 1940, it was 45.8 sec. Let R(t) = the record in the race and t = the number of years since a) Find a linear hction that fits the data. b) Use the Mction in (a) to predict the record in 2003 and in c) Find the year when the record will be sec. 1 Find a linear hction that fits the data. R(t) = (Round to the nearest hundredth.) What is the predicted record for 2003? [7 sec (Round to the nearest hundredth.) What is the predicted record for (Round to the nearest hundredth.) sec In what year will the predicted record be seconds? (Round to the nearest year.) ,-. In 1994, the life expectancy of males in a certain country was 64.7 years. In 2000, it was 68.4 years. Let E represent the life expectancy in year t and let t represent the number of years since The linear function E(t) that fits the data is (Round to the nearest tenth.) Use the bction to predict the life expectancy of males in (Round to the nearest tenth.) Page 12