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
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.
Task 1a: Let's research the rates of two different cab companies in New York City. Company A charges a flat fee of $3 for picking someone up and an additional fee of $2 per mile driven.
Task 1b: To express the cost of the cab ride from Company A using an equation, we can use the slope-intercept form: y = mx + b. In this case, y represents the total cost of the ride, x represents the number of miles driven, m represents the charge per mile ($2), and b represents the flat fee ($3). The equation would be y = 2x + 3. I chose the slope-intercept form because it directly represents the cost as a function of the number of miles driven.
Task 1c: In the context of this problem, the x-intercept of the equation represents the number of miles driven when the total cost of the ride is $0. However, in this case, the x-intercept is not meaningful since the minimum cost of a ride is the flat fee of $3. The y-intercept, $3, represents the cost of stepping into the cab regardless of the number of miles driven.
Task 2a: Let's research the rates of another cab company, Company B, in New York City. Company B charges a flat fee of $5 for picking someone up and $1.50 per mile driven.
Task 2b: To express the cost of the cab ride from Company B in a table given the number of miles driven, we can use the equation y = mx + b, where y represents the total cost of the ride, x represents the number of miles driven, m represents the charge per mile ($1.50), and b represents the flat fee ($5). I chose the slope-intercept form again because it directly represents the cost as a function of the number of miles driven.
Number of Miles (x) | Total Cost of Cab Ride (y)
0 | $5
1 | $6.50
2 | $8
3 | $9.50
... | ...
Task 3a: Let's create a table showing the average gas price each year.
Year | Average Gas Price ($)
2015 | $2.50
2016 | $2.30
2017 | $2.40
2018 | $2.60
2019 | $2.80
Task 3b: Let's create a scatter plot of the data in the table.
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2015 2016 2017 2018 2019
Task 3c: The equation that models the data could be y = -0.05x + 107. The domain of this equation would be the years from 2015 to 2019, and the range would be the average gas prices. I determined this equation by finding the best-fit line through the scatter plot data.
Task 3d: From the scatter plot, there seems to be a negative correlation, as the gas prices generally decrease over the years. In 2020, based on the trend observed, we could expect the gas price to be lower than the price in 2019, possibly around $2.70 or less.