1. Suppose you are at the 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: C(g) = 3.5 (g)
a) Find C(2) (2 pts.)
b) Find C(5) (2 pts.)
2. Suppose that the linear equation y = 0.3x + 0.9 represents an estimate of the average cost of gas for year x starting in 2002. The year 2002 would be represented by x = 1, for example, as it is the first year in the study. Similarly, 2008 would be year 7, or x = 7.
a) What year would be represented by x = 2? (2 pts.)
b) How much did it cost per gallon of gasoline in the year represented by x=2? (2 pts.)
c) What x-value represents the year 2011? (2 pts.)
d) Assuming this growth trend continues, what will the price of gasoline be in the year 2011? How did you arrive at your answer? Show your work (2 pts.)
3. Suppose the line y = 0.3x + 0.9 represents an estimate of the average cost of gasoline for each year and the line 0.2x – y = -0.8 estimates the price of gasoline in January of each year.
a) What are the slopes of each of these two lines? (2 pts.)
b) Are the lines intersecting, parallel, or perpendicular? Explain your reasoning. (1 pt.)
We do not do your work for you. Once you have answered your questions, we will be happy to give you feedback on your work. Although it might require more time and effort, you will learn more if you do your own work. Isn't that why you go to school?
1. a) To find C(2), substitute 2 for g in the equation C(g) = 3.5(g):
C(2) = 3.5(2)
= 7
Therefore, C(2) = 7.
b) To find C(5), substitute 5 for g in the equation C(g) = 3.5(g):
C(5) = 3.5(5)
= 17.5
Therefore, C(5) = 17.5.
2. a) To find the year represented by x = 2, simply add 1 to x:
Year = 2002 + (2 + 1)
= 2002 + 3
Therefore, the year represented by x = 2 is 2005.
b) To find the cost per gallon of gasoline in the year represented by x = 2, substitute 2 for x in the equation y = 0.3x + 0.9:
y = 0.3(2) + 0.9
= 0.6 + 0.9
= 1.5
Therefore, the cost per gallon of gasoline in the year represented by x = 2 is $1.50.
c) To find the x-value that represents the year 2011, subtract 2002 from 2011:
x = 2011 - 2002
Therefore, the x-value that represents the year 2011 is 9.
d) Assuming the growth trend continues, we can find the price of gasoline in the year 2011 by substituting x = 9 into the equation y = 0.3x + 0.9:
y = 0.3(9) + 0.9
= 2.7 + 0.9
= 3.6
Therefore, the price of gasoline in the year 2011, according to the growth trend, is $3.60.
3. a) The slope of the line y = 0.3x + 0.9 is 0.3.
The slope of the line 0.2x - y = -0.8 can be found by rearranging the equation in slope-intercept form (y = mx + b):
0.2x - y = -0.8
-y = -0.2x - 0.8
y = 0.2x + 0.8
Therefore, the slope of the line 0.2x - y = -0.8 is 0.2.
b) To determine if the lines are intersecting, parallel, or perpendicular, we need to compare their slopes.
The slopes of the two lines (0.3 and 0.2) are not equal, so the lines are not parallel.
The slopes are also not negative reciprocals of each other, so the lines are not perpendicular.
Therefore, the lines are intersecting.