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College Math 116 Week 6 Answer Guide- Algebra 1A -

Week Six Algebra 1A study guide and Soultions

1. Imagine you are at a gas station filling your tank with gas. The function C(g) represents the cost of filling up the gas tank with gallons of regular gasoline. Given the equation

C(g) = 3.03(g)

a. What does the number 3.03 represent?

The value 3.03 represents the cost per gallon of gas.

b. Find C(2).


c. Find C(9).


d. For the average motorist, name one value for that would be inappropriate for this function’s purpose. Explain why you chose that number.

100 is inappropriate because the typical motorist will not have a 100-gallon tank.

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

= {0 £ £ 20} = {0 £ £ $60.60}

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.




2006 1997

2.31 1.26 = =


= - m

To arrive at this answer, subtract the y-values from each of the coordinates and place the value of the

difference in the numerator. Then subtract the x-values from each of the coordinates and place the

difference in the denominator. Finally, simplify by dividing the numerator by the denominator.


3. The linear equation

= 0.15+ 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 = 1, for example, because it is the first year in the study. Similarly, 2005 would be year 9, or = 9.

a. What year would be represented by = 4?


b. What x-value represents the year 2018?

= 22

c. What is the slope, or rate of change, of this equation?

= 0.15

d. What is the y-intercept?

= 0.79

e. What does the y-intercept represent?

The y-intercept represents the average price of gas in 1996 (when = 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?

The price of gasoline in 2018 will be $4.09 per gallon if the trend continues. This answer can be found by substituting the answer from Part a (x=22) for the x value in the equation.

= 4.09

4. The line

= 0.15+ 0.79 represents an estimate of the average cost of gasoline each year. The line 0.11= -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.

Answers may vary. You must support your answer with a logical reason. DO NOT CHOOSE PERPENDICULAR.

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 and the slope of the second equation is 0.11. Since the slopes are not equivalent, the lines are intersecting and not parallel.


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