1. Imagine you are at a gas station filling your tank with gas. The function C(g

Question

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
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 that number.

e. If you were to graph C(g), what would be an appropriate domain and range? Explain your reasoning.

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.

3. The linear equation y = 0.15 x + 0.79



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?

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?

e. What does the y-intercept represent?

f. Assuming this growth trend continues, what will the price of gasoline be in the year 2018? How did you arrive at your answer?


4. The line y = 0.15 x + 0.79



represents an estimate of the average cost of gasoline each year. The line
0.11x - y = -0.85


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.

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?

Explanation / Answer

1. The equation didn't show up but I will imagine it's
c(g)=3.03g
(a) 3.03 represent the cost of a gallon of gas
(b) C(2)= 3.03(2) =6.06
(c) C(9)= 3.03(9)=27.27
(d) -1, You can't pump a negative amount of gasoline out of a pump
(e) domain is from 0 to infinity and the range is from 0 to infinity. If one were to reason that someone pumping gas can have a maximum gas tank capacity of 20 gal then the domain is 0 to 20 and the range is from 0 to 60.60

2. The slope is (y2-y1/x2-x1) = (2.31-1.26)/ (2006-1997)

3.

(a) if 1997 is 1, then since 4 is 3 years past 1997, it represents 2000

(b)2018 is 21 years past 1997, and since 1997 is 1, 1+21=22. x=22

(c).15

(d).79

(e) initial cost in 1997

(f) c(x)=.15(22)+.79=4.09

4.

(a) The cost starts lower and has a greater slope than the price, therefore the lines will eventually intersect. As a consequence of two lines being perpendicular, their slopes have to have opposite signs, that is not the case here

(b) The lines have different slopes and therefore are not parallel

(c) My expectation was based on already having known they weren't parallel. It wasn't a contradiction.

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