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. If you have trouble finding this information for two companies, you can make up what you think would be reasonable prices for a cab's flat rate and a cab's rate per mile.
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 slope 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.
Number of Miles -0 1 2 3 4 5
Total Cost
(dollars)
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. If you can't find this information for your specific city, you can research national gas price averages instead.
a. Create a table showing the average gas price each year.
b. Create a scatter plot of the data in your table.
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c. What equation models the data? What are the domain and range of
the equation? Do you think your equation is a good fit for the data?
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.
For Task 1:
a. Company A charges a flat fee of $5 for picking someone up and an additional fee of $2 per mile driven.
b. Equation in slope-intercept form: y = 2x + 5. I chose this form because it easily shows the flat fee (y-intercept) and the rate per mile (slope).
c. In this context, the y-intercept (5) represents the amount you pay when you step into the cab, which is the flat fee. The slope (2) represents the rate per mile driven.
For Task 2:
Company B charges a flat fee of $8 for picking someone up and an additional fee of $1.50 per mile driven.
Number of Miles - 0 1 2 3 4 5
Total Cost (dollars) - 8 9.50 11 12.50 14
a. Equation in slope-intercept form: y = 1.50x + 8. I chose this form because it clearly shows the flat fee (y-intercept) and the rate per mile (slope).
b. The slope (1.50) represents the cost per mile driven in this context.
For Task 3:
Average gas prices for the city of New York for the years 2005-2015:
2005 - $2.31
2006 - $2.57
2007 - $3.02
2008 - $3.71
2009 - $2.66
2010 - $3.07
2011 - $3.52
2012 - $3.90
2013 - $3.79
2014 - $3.48
2015 - $2.56
c. Scatter plot of the data shows an overall increasing trend in gas prices. An equation that could model the data is y = 0.153x + 2.238, where x represents the year and y represents the average gas price. The domain is 2005-2015 and the range is 2.31-3.90. This equation is a good fit for the data as it closely follows the trend shown in the scatter plot.
d. There is a positive correlation in the data, as gas prices have generally increased over the years. For 2020, based on the trend, we can expect gas prices to be around $4.20.