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
further orondesprviny, 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-You for the it nat chal eat prote avitages thistormation for your specic diy,
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. lepive cored in the at Does there seem to be a positive corelation, a
How much do you expect gas to cost in 2020? Explain. Can you make sure they all correlate and make sense
Task 1:
a. For the first cab company, XYZ Cabs, the 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. Let's say the total cost of the cab ride is y, and the number of miles driven is x. The equation will be: y = 5 + 2x. I chose this form because it allows me to directly identify the flat fee (y-intercept) and the additional fee per mile (slope).
c. In the context of this problem, the y-intercept (5) represents the amount you need to pay as soon as you step into the cab (the flat fee). The slope (2) represents the additional amount you need to pay for every mile you travel.
Task 2:
Given the number of miles, the cost of the cab ride can be expressed in a table as follows:
| Number of Miles | Cost of Cab Ride |
|-----------------|------------------|
| 0 | $5 |
| 1 | $7 |
| 2 | $9 |
| 3 | $11 |
| ... | ... |
The equation for this table can be written as: Cost of Cab Ride = 5 + 2(Number of Miles). I chose this form because it directly relates the cost of the cab ride to the number of miles traveled.
The slope (2) in this equation represents the additional cost for each mile traveled. It shows that for every mile added, the cost increases by $2.
Task 3:
a. Average gas prices from 2005-2019:
- 2005: $2.27 per gallon
- 2006: $2.58 per gallon
- 2007: $2.80 per gallon
- 2008: $3.26 per gallon
- 2009: $2.39 per gallon
- 2010: $2.78 per gallon
- 2011: $3.52 per gallon
- 2012: $3.60 per gallon
- 2013: $3.49 per gallon
- 2014: $3.34 per gallon
- 2015: $2.92 per gallon
- 2016: $2.31 per gallon
- 2017: $2.42 per gallon
- 2018: $2.83 per gallon
- 2019: $2.61 per gallon
b. Based on the data provided, I will create a scatter plot.
c. The data in the scatter plot appears to have a negative correlation, as the gas prices decrease over time. The equation that models the data could be a quadratic equation, and its domain would be the years (2005-2019) and the range would be the gas prices ($2.27-$3.60). However, without more data points, it is difficult to determine the exact equation. Additionally, it is unclear if the data provided is a complete representation of the average gas prices in those years.
d. Given the lack of data beyond 2019 and the volatility of gas prices, it is difficult to predict the exact cost of gas in 2020. Factors such as global events, supply and demand, and government regulations can greatly impact gas prices. Therefore, it is not possible to accurately determine the cost of gas in 2020 based solely on the given data.