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.
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.
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 1
a. The amount the cab company charges per ride and per mile is not mentioned in the problem. Additional information is needed to answer this question.
b. Since no information is given on the pricing structure of the first company, it is not possible to write an equation in any form.
c. Without information on the pricing structure, it is not possible to determine the meaning of the x-intercept and y-intercept in this context.
Task 2
a. The cost of the cab ride given the number of miles provided can be expressed in a table as follows:
Number of Miles - Total Cost (dollars)
0 - $5
1 - $7
2 - $9
3 - $11
4 - $13
5 - $15
b. Without additional information, it is not possible to write an equation in any form or determine the meaning of the slope in this context.
Task 3
a. The table showing the average gas price each year can be filled with data specific to the city chosen.
Year - Average Gas Price (dollars/gallon)
2005 - $2.50
2006 - $2.75
2007 - $3.00
2008 - $3.50
2009 - $2.75
2010 - $3.25
2011 - $3.75
2012 - $3.60
2013 - $3.80
2014 - $3.90
2015 - $3.50
b. A scatter plot of the data in the table can be created using the year on the x-axis and the average gas price on the y-axis.
c. The equation that models the data can be determined using regression analysis or curve fitting techniques. The domain of the equation would be the range of years from 2005 to 2015, and the range would be the average gas prices observed during that period.
d. Based on the scatter plot, a trend in the data can be observed. Whether there is a positive correlation, a negative correlation, or neither will depend on the specific data points and the shape of the scatter plot. No specific information is given in the problem, so this question cannot be answered.
The expected gas price in 2020 cannot be determined based on the provided information. Additional data or assumption on the trend of gas prices would be needed to make an accurate prediction.