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 Interpreting Data of Alcohol-Related Traffic Accidents

Activity Description

Activity Guide

           Part 1: Creating an algebraic system.

According to the National Highway Traffic Safety Administration, during 1999 the percent of alcohol-related deaths (in relation to total traffic deaths) in Washington DC was approximately 54%. During 2000, a total of 49 people died in traffic accidents, 19 of which were alcohol-related. The combined alcohol-related deaths for both years were approximately 46%.

1.  Let x represent the total number of traffic deaths and y the number of people killed in alcohol-related accidents in DC during 1999.  Using a system of equations, solve for x and y and interpret your results. 

 

2. Discuss the appropriateness of your answers in the context of task 1. What could be possible solutions for task 1?

 

3. What range of values would be reported as 54% if this percentage was rounded to the nearest whole percent? What about 46%?

 

4. Construct a system of inequalities using the results from tasks 1 and 3. Write each inequality for y in terms of x (e.g., y< .545x).

 

Part 2: Numerical representation.

5.  Using Fathom create a table that models the system in task 4.

How to create a table and enter data: 

  1. To insert an empty case table either:

    1. Click Insert, then click Case Table; or

    2. Click, hold, and grab the Case Table icon (below the Display on the menu bar), and drag it to the workspace.

  2. To enter an attribute click on <new>, type in the first attribute (e.g., X), and hit Enter. Note: Attribute names must be one word.

  3. Repeat this process to enter all attributes. Note: You may drag the edges of the table or the attribute boxes to make them wider.

  4. To title this table, double click on the label Collection 1, type in the title, and hit OK.

  5. Enter data in the empty cells. Use Tab to move to the next cell.

  6. Save your file by clicking File then Save.

Note: You may always undo or redo changes by clicking Edit, then either Undo, or Redo.

            

Figure 1. Screenshot of the formula line in Fathom.

How to enter a formula: 

  1. To enter a formula click on <Display>, <Show Formulas>.

  2. Double click and enter the formula in the empty cells below each attribute.  Click <Apply> and <OK> when you have finished entering the formula. Use Tab to move to the next cell. Repeat this process for each formula.

 

How to enter a sequence of whole numbers from 1 to N: 

  1. Double click and enter the formula in the empty cells below an attribute.  Double click on  <Specials>  and then <caseIndex> in the formula editor. Click <Apply> and <OK>.  In order to specify N click on <Data> in the menu bar, <New Cases> and type in a value for N. This will allow you to fill in the attribute column numbers from 1 to N.

6.  Using the table of values, sketch the graphs and label the y-intercepts. What is an appropriate area (window) to determine all possible solutions of this problem?

 

 

 

 

7.  Using Fathom graph all four functions. Figure 2 shows how your graph will look prior to any window and scale adjustments. Why do you think the lines are so close to each other? What part of this graph is the most important in solving this problem? Why?

How to show multiple graphs on one coordinate system: 

  1. Grab and drag the graph icon into your Fathom document.

  2. Change <Empty Plot> to a <Function Plot> in the right corner of the graph window.

  3. Go to <Graph>, then <Plot Function>.

  4. Type in your function then click <Apply>, <OK>, and close that window.

  5. Repeat steps 3 & 4 for each function.

 

 

Figure 2. Screenshot of the function plot in Fathom.

8. Using the appropriate window discussed in step 6, adjust the scale of the graph by dragging either axis (see Figure 3). Is there only one solution to this problem? Why or why not? What do the x- and y-axis represent?

       

Figure 3. Screenshot of the rescaled function plot in Fathom.

9. Approximate the domain and range of the feasible region (see Figure 4) of the graphs. What type of numbers can represent the solutions of this problem?

 

           

Figure 4. The feasible region of the graphs.

10.  List all possible solutions by finding lattice points in the feasible region. For example, (52,28) is a lattice point since both values are integers. Describe your strategy for finding all lattice points.

 

Figure 5. Screenshot of partial table in Fathom.

Solutions: (41, 22); (46,25); (48,26); (50,27); (52,28)

11.  Explain what each of the coordinates mean in the context of this problem. Can you eliminate any of the solutions? Why or why not?


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Last modified on March 6, 2002.