Cab companies often charge a flat fee for picking someone up and then charge an
additional fee per mile driven. Pick a U.S. city and research the rates of two
different cab companies in that city. Find companies that charge different amounts
per mile and have different flat fees.
Task 1
a. For the first company, express in words the amount the cab company
charges per ride and per mile.
b. Write an equation in slope-intercept, point-slope, or standard form. Explain
why you chose the form you did.
c. What do the x-intercept and y-intercept mean in the context of this problem?
Hint: What do you pay when you step into the cab?
Task 2
For the second company, express in a table the cost of the cab ride given the number of miles provided.
a. Write an equation in slope-intercept, point-slope, or standard form. Explain
why you chose the form you did.
b. What does the slope mean in the context of the problem?
Task 3
Cabs use a valuable commodity—gas! Research average gas prices from 2005–
2015 for the city you chose.
a. Create a table showing the average gas price each year.
b. Create a scatter plot of the data in your table.
c. What equation models the data? What are the domain and range of
the equation? Explain how you determined your answers.
d. Is there a trend in the data? Does there seem to be a positive correlation, a
negative correlation, or neither?
How much do you expect gas to cost in 2020? Explain.
bro just help me out 💀
Have you at least done step 0?
Pick a U.S. city and research the rates of two different cab companies in that city. Find companies that charge different amounts per mile and have different flat fees.
Till you do that, there's nothing I can do for you.
Task 1:
a. To get the information about cab companies in a particular city, you can research online by visiting their official websites or by using online directories that provide information about local businesses. Choose a U.S. city, such as New York City or Chicago, and search for two different cab companies in that city. Look for their pricing information, including the flat fee for picking someone up and the additional fee per mile driven. Note down the rates of both companies.
b. To write an equation representing the first company's pricing structure, you can use the slope-intercept form (y = mx + b) of a linear equation. Here, x represents the number of miles and y represents the cost of the ride. The equation will be in the form y = mx + b, where m is the charge per mile and b is the flat fee.
The slope-intercept form is chosen because it allows us to represent the cost of the ride (y) as a linear function of the number of miles (x), with m representing the rate per mile and b representing the initial fixed fee.
c. In the context of this problem:
- The x-intercept represents the number of miles at which the cost of the ride becomes zero. This means that when x equals the x-intercept value, there is no additional charge for the miles covered, and the rider only pays the flat fee.
- The y-intercept represents the initial cost of getting into the cab. When the number of miles is zero, the cost of the ride will be equal to the y-intercept value, which is the flat fee.
Task 2:
a. To express the cost of the cab ride given the number of miles in a table, create a table with two columns: "Number of Miles" and "Cost of the Ride." Using the rates of the second cab company that you researched, calculate the cost of the ride for various numbers of miles and enter the values in the table.
b. To write an equation representing the second company's pricing structure, you can use the standard form (Ax + By = C) of a linear equation, where A, B, and C are constants. In this case, x represents the number of miles, and y represents the cost of the ride. The equation will be in the form x + By = C, where B represents the rate per mile and C represents the flat fee.
The standard form is chosen because it provides a general representation of a linear equation, where the coefficients A, B, and C can be used to represent different rates and fees for different companies.
c. The slope (B) in the standard form equation represents the rate per mile. It indicates how much the cost of the ride increases for each additional mile.
Task 3:
a. To research average gas prices from 2005-2015 for the chosen city, you can refer to historical gas price data from reliable sources like the U.S. Energy Information Administration (EIA) or other reputable databases. Look for the average gas prices for each year from 2005 to 2015 and create a table showing this information.
b. To create a scatter plot of the gas price data, use a graphing tool or software that allows you to plot points. Each year will be plotted on the x-axis, and the average gas price for that year will be plotted on the y-axis.
c. To determine the equation that models the data, you need to analyze the scatter plot and decide if a linear, quadratic, exponential, or other type of equation best fits the data. If the scatter plot shows a linear pattern, you can use the method of least squares to find the equation of the best-fit line. The domain of the equation will be the range of years considered (2005-2015), while the range of the equation will be the range of gas prices observed during that time.
d. Analyze the scatter plot to identify any trends in the data. If there is a positive correlation, it means that gas prices tend to increase as the years go by. If there is a negative correlation, it means that gas prices tend to decrease over time. If there is no apparent pattern, there is no correlation. Use your observations from the scatter plot to determine whether there is a trend and whether it is positive, negative, or neither.
To estimate the gas price in 2020, you can extend the line of best fit on the scatter plot or use the equation derived from the data to evaluate the gas price at that particular year.