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
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 represents an estimate of the average cost of gasoline each year. The line
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?
Please Help??
Please show your work. A little thinking on your part should answer a lot of these.
In 1., isn't an equation missing?
There is nothing with a 3.03 in it.
That number looks like a typical price per gallon of gasolie.
1a. In the equation C(g), the number 3.03 represents the cost of filling up the gas tank with 1 gallon of gas. This is because the equation C(g) gives the cost of filling up the tank with g gallons, and in this case, g = 1, so the number 3.03 represents the cost of 1 gallon of gas.
b. To find C(2), you simply substitute 2 for g in the equation C(g). So, C(2) = 3.03 * 2.
c. To find C(9), you substitute 9 for g in the equation C(g). So, C(9) = 3.03 * 9.
d. For the average motorist, a value of g that would be inappropriate for this function's purpose could be a negative value, such as -2. This is because you cannot have a negative number of gallons of gas, so a negative value for g does not make sense in the context of this function.
e. If you were to graph C(g), an appropriate domain would be the set of non-negative real numbers since you cannot have a negative number of gallons of gas. So, the domain would be [0, ∞). The range would be the set of non-negative real numbers as well, since the cost of filling up the gas tank will always be a positive value. So, the range would also be [0, ∞).
2. To find the slope, or rate of change, between the points (1997, 1.26) and (2006, 2.31), you use the formula: slope = (y2 - y1) / (x2 - x1). In this case, y1 = 1.26, y2 = 2.31, x1 = 1997, and x2 = 2006. You substitute these values into the formula and calculate the slope.
3a. Since x represents the year, when x = 4, it would represent the year 1997 + 4 = 2001.
b. To find the x-value that represents the year 2018, you need to subtract 1997 from 2018. So, x = 2018 - 1997 = 21.
c. The slope, or rate of change, of the equation is the coefficient of x in the equation. So, the slope is 0.134.
d. The y-intercept is the value of y when x = 0. In this equation, the y-intercept is -9.87.
e. The y-intercept represents the estimated average cost of gas in the starting year of the study (1997). In this case, the y-intercept of -9.87 would represent the estimated average cost of gas in 1997.
f. To estimate the price of gasoline in the year 2018, you substitute x = 21 (as determined in part b) into the equation. So, you calculate y = 0.134 * 21 - 9.87.
4a. Since both lines represent estimates of the average cost of gasoline each year, it is expected that the lines would be parallel. This is because they both represent the same trend and have the same rate of change.
b. To determine if the lines are parallel, you compare the slopes (coefficients of x) in the equations. If the slopes are the same, then the lines are parallel. If the slopes are different, then the lines are not parallel. You compare the slopes in the equations to determine if they are parallel.
c. The answer to part b would confirm the expectation in part a. If the slopes are the same, then the lines are parallel, which aligns with the initial expectation. If the slopes are different, then the lines would not be parallel, contradicting the initial expectation.