math

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 to your hard drive by selecting Save As from the menu . Click the white space below each question to maintain proper formatting What does the number 3 .03 represent

p 3 .03 represents the the price /cost of gas per gallon

Find C (2

C (2 3 .03 (2 6 .06

Find C (9

C (9 3 .03 (9 27 .27

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

A negative number , say -1 , will be inappropriate for the purpose of this function . We are buying a positive number , or at all , of gallons of gas

If you were to graph C (g , what would be an appropriate domain ? Range Explain your reasoning

The domain and range of C (g ) would be all positive real numbers including 0 since it may be possible to purchase an infinite number of gallons of gas , or at all and in which case the cost /price is also 0

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 (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

For simplicity , let (x1 , y1 (2006 , 2 .31 ) and (x2 , y2 (1997 , 1 .26

m (y1 - y2 (x1 - x2 (2 .31 - 1 .26 (2006 -1997 1 .05 / 9 0 .117

The linear equation represents an estimate of the average cost of gas for year x starting 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

What year would be represented by x 4 ? year 2000

What x-value represents the year 2018 ? x 22

What is the slope (or rate of change ) of this equation ? m 0 .15

What is the y-intercept ? b 0 .79

What does the y-intercept represent

y-intercept is the value of y when x 0 and could represent the cost of gas prior to 1997

Assuming this growth trend continues , what will the price of gasoline be in the year 2018 ? How did you arrive at your answer we solve for y when x 22

y 0 .15 (22 0 .79 3 .3 0 .79 4 .09

The line represents an estimate of the average cost of gasoline for each year...