Appendix E 7-31-10
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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. 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? Cost per gallon
b. Find C(2). C(2) = 3.03(2) = 6.06
c. Find C(9). C(9) = 3.03(9) = 27.27
d. For the average motorist, name one value for g that would be inappropriate for this functions purpose. Explain why you chose that number.
G cannot be a negative number because gas tanks do not have negative gallons.
e. If you were to graph C(g), what would be an appropriate domain and range? Explain your reasoning.
The domain should go from g = 0 to g = 20. The average gas tank is 20 gallons or smaller.
The range would then go from C = 0 to C = 50 which represent the cost for purchasing between 0 and 20 gallons.
2. Examine the rise in gasoline prices from 1997 to 2006. 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 (“Consumer price index,” 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.
Slope = rise/run
We divide the change in the gas price (rise) by the number of years that have elapsed
3. The linear equation
[pic]
represents an estimate of the average cost of gas for year x starting in 1997 (“Consumer price index,” 2006). The year