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
1
2
3
4
5
of Miles
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.
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. Make sure it makes sense and correlates
Task 1
a. For the first company, let's say the cab company charges a flat fee of $5 for picking someone up and an additional fee of $2 per mile driven.
b. I will write the equation in slope-intercept form, which is y = mx + b. In this case, the equation would be: cost = 2m + 5. I chose this form because it allows me to easily calculate the total cost based on the number of miles driven.
c. In this context, the slope represents the rate at which the cost increases per mile driven. In this case, the slope is 2, indicating that for every mile driven, the cost increases by $2. The y-intercept of 5 represents the flat fee charged when stepping into the cab.
Task 2
For the second company, let's express the cost of the cab ride in a table given the number of miles provided:
Number of Miles Total Cost (dollars)
1 10
2 18
3 24
4 28
5 30
a. Since the data is given in a table format, I will choose to write the equation in standard form: cost = mx + b. In this case, the equation would be: cost = 2m + 8. I chose this form because it allows me to directly calculate the total cost based on the number of miles driven.
b. The slope of 2 in this context indicates that for every mile driven, the cost increases by $2.
Task 3
a. Let's create a table showing the average gas price each year:
Year Average Gas Price (dollars)
2005 2.28
2006 2.58
2007 2.81
2008 3.27
2009 2.36
2010 2.78
2011 3.53
2012 3.60
2013 3.50
2014 3.36
2015 2.43
b. Based on the data, I will create a scatter plot.
c. The data shows a general trend of fluctuation in gas prices. To model the data, I will use a polynomial regression equation, such as y = ax^2 + bx + c. The domain of the equation would be the years (2005-2015), and the range would be the average gas prices. However, analyzing the scatter plot, it is clear that a simple linear equation may not be the best fit for this data. A quadratic equation or a higher degree polynomial might be better suited to capture the fluctuations in gas prices over time.
d. Analyzing the scatter plot, there doesn't seem to be a clear positive or negative correlation. However, there are noticeable fluctuations in gas prices, suggesting that the price is influenced by other factors beyond a simple linear relationship.
As for the expected gas price in 2020, it is difficult to predict. However, based on the general trend of the data, it is reasonable to expect that gas prices will continue to fluctuate and be influenced by various economic and political factors.