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Date Created: 11/16/15
Axia College Material 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 Cg represents the cost C of filling up the gas tank with g gallons Given the equation Cg 303g a What does the number 303 represent The 303 represents the price in dollars per gallon of gas b Find C2 Plug in 2 for g C2 303gtlt 2 606 c Find C9 Plug in 9 for g C9 303x9 2727 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 G cannot be 2 or O because you can t put a negative number of gallons into your gas tank e If you were to graph Cg what would be an appropriate domain Range Explain your reasoning The domain should go from g 0t0g 20 You cannot have a negative number for the number of gallons so g must be 0 or greater Most gas tanks are less than 20 gallons so 20 would be a good upper limit MAT 116 The range would then go from C 0 to C 606 which are the prices for getting between 0 and 20 gallons Examine the rise in gasoline prices from 1997 to 2006 The price of regular unleaded gasoline in January 1997 was 126 and in January 2006 the price of regular unleaded gasoline was 231 Bureau of Labor Statistics 2006 Use the coordinates 1997 126 and 2006 231 to find the slope or rate of change between the two points Describe how you arrived at your answer Slope riserun We divide the change in the gas price rise by the number of years that have elapsed run Slope 231 126 105 7 2006 1997 9 60 7 The gas prices increase by a of a dollar per year that s nearly 12 cents per year 3 The linear equation y 015x 079 represents an estimate of the average cost of gas for year xstarting in 1997 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 If 1997 is 1 then we need 3 years later which is the year 2000 b What x value represents the year 2018 Subtract 1996 to get the x value 2018 1996 22 c What is the slope or rate of change of this equation The slope is 015 d What is the y intercept The y intercept is 079 e What does the y intercept represent The y intercept is the gas price in 1996 when x 0 MAT 116 f Assuming this growth trend continues what will the price of gasoline be in the year 2018 How did you arrive at your answer To get the gas price in 2018 plug x 22 into the equation Price 015gtlt 22 079 409 4 The line y 015x 079 represents an estimate of the average cost of gasoline for each year The line 01 1x y O85 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 I might expect them to be parallel That s because the increase in the average gas price per year should increase at the same rate as the price in each January each year b Use the equations of the lines to determine if they are parallel What did you find The slope of the first equation is 0 15 Solve the second equation for y to get the slope y 011x085 The slope is O 1 1 so they are not parallel c Did your answer to part b confirm your expectation in part a No the answer is part b did not confirm my expectation The information that went into building these two equations must have come from separate sources References Bureau of Labor Statistics 2006 Consumer price index Retrieved June 1 2007 from httpdatablsgovcgibinsurveymostap MAT 116
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