Associate Level Material
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.
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. Imagine you are at a 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 [pic]
a. What does the number 3.03 represent? 3.03 represents the price that it costs per gallon of gas.
b. Find C(2).=3.03(2)3.03+3.03=6.06
31) to find the slope, or rate of change, between the two points. Describe how you arrived at your answer. Slope=rise/run
we divide the change in the gas price (rise) by the number of years that has elapsed (run)=(2.31-1.26)/(2006-1997)=1.05/9 =7/60
The gas prices increases by 7/60 of a dollar per year that’s nearly 12 cents per year
3. The linear equation
represents an estimate of the average cost of gas for year x starting in 1997 (“Consumer price index,” 2006). The year 1997 would be represented by x = 1, for example, because 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.=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 0.15
d. What is the y-intercept? 0.79
e. What does the y-intercept represent? The gas price in 1996, when x=0
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 =0.15*22+0.79=$14.09
4. The line
represents an estimate of the average cost of gasoline each year. The line
estimates the price of gasoline in January of each year (“Consumer price index,” 2006).
a. Do you expect the lines to be intersecting, parallel, or perpendicular? Explain your reasoning. Parallel because the increase in the average gas price per year should increase at the same rate as the price in each January in 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=0.11x+0.85. The slope is 0.11 so they are not parallel.
c. Did your answer to Part b. confirm your expectation in Part a? no it did not.
Bureau of Labor Statistics. (2006). Consumer price index. Retrieved from http://data.bls.gov/cgi-bin/surveymost?ap