Analyzing Carbon Dioxide Levels in the Earth's Atmosphere

 

 

 

The Problem:

 

By examining carbon dioxide levels in the Earth's atmosphere over the past 200+ years, can we predict carbon dioxide levels for the future?  How have the levels of carbon dioxide changed over the past 100 years, and why might the change in levels for different time periods vary?

 

 

 


Data that are in tabular form can be downloaded from the web to a TI-83+ graphing calculator.  These directions were adapted from a December 2001 Mathematics Teacher article by Daren Starnes.

 

 

 

 

 


 

Harvesting the Data:

Downloading data from a web site to a computer.

 

  1. Create a new folder on the computer desktop.  

To do this, right click on the desktop.  Move down to the option New, and left click on Folder.  (All remaining ãclickä directions refer to left "clicks" unless otherwise indicated.)

 

  1. Give the folder a name. 

If the name of the folder is highlighted, simply type the new name.  If the name of the folder is not highlighted, double click on the name of the folder and then name it.  For this example, use the name CO2.

 

  1. Create and name a new text document.

Double click on the folder and under File, click on New.  Next, click on text document.  For this example, name the document CO2Data.txt.  With Windows 98, you must give it a name ending with .txt.  This differentiates a text document from a word document. 

 

  1. Minimize the window. 

This command is found in the upper right hand corner of the window.  There are three "boxes."  Of the three boxes, choose the one on the left with the underline symbol.

 

  1. Open Internet Explorer and in the space labeled Address, type in http://exploringdata.cqu.edu.au/datasets.htm and then press Enter. 

 

On the opening screen (below left), click on the right column (under Tab) on the row for the Carbon Dioxide data.  This takes you to the Carbon Dioxide data set similar to the screen below right.

   

 

  1. Highlight the data.

To highlight the data, hold down the left mouse button and drag down and to the right.  Do not highlight the words.  Be sure that all data are highlighted.

 

  1. Copy and paste the data into your text document.

      Click on Edit on the top command line and choose Copy.

Click on the CO2 folder on the bottom command line of the computer screen.    Open the text document CO2Data by double clicking on it.

Click on Edit on the top command line and choose Paste.

 

 

  1. Save the data file (as text) and note the number of rows and columns of data.

Click on File at the top command line and choose Save.  Before you leave the text document, note the number of rows and the number of columns in the data set.

 

  1. Close the text document, the folder and Internet Explorer. 

The Close command is found in the upper right hand corner of the window.  There are three "boxes."  Of the three boxes, choose the one on the right with the x symbol.

 

  1. Open TI Graph Link. 

From the Start menu (at the bottom left corner of the screen), choose Programs and then choose TI Graph Link.  Click on TI Graph Link 83 Plus.   Do not click on the TI Graph Link 83 Plus Help.

 

 

  

  1.  Import the C02 data from the text file to Graph Link

a.       From the top command line of Graph Link, click on Tools and, under Tools, choose Import ASCII Data.  On the screen that appears (below left), choose a matrix name.  Use A for this example.   Enter the number of rows and columns of the data set.  Click on OK.

  

 

b.      You must now locate the text document.  Double click on c:\, then Windows, then Desktop, and then the name of the folder (co2).

 

c.       Now, double click on the name of the data set (co2dat~1.txt ) in the left Graph Link window.  The name of the matrix will appear.  Click OK. 

 

d.      The data should now be shown in the right window of the Graph Link screen similar to the figure below.

 

 

 

 

 

Transferring the data to the graphing calculator:

 

  1. Be sure that the Graph Link cable is firmly connected to the back of the computer and to the bottom of the calculator.  Turn the calculator on.  To link, you should be on the home screen of the calculator.  Press the yellow 2nd key followed by the MODE key to access the home screen. 

 

  1. At the top of the Graph Link command line, choose Link and move down to Cable Type.  Be sure that the color of the cable selected matching the color of the cable youâre using.

 

  1. Select Link and choose Send to.  Then, move to and choose Send to RAM.

 

  1. Double click on the letter name of the matrix.  If you chose A for the name of the matrix, a.8xm is the file name.  The name of the matrix should be pasted in the File selected box at the bottom of the screen. 

 

 

  1. Click OK.  You will see a "Sending" box.  When it says ãCompleted,ä click OK and then close the Graph Link Screen.

 

  1.  Moving the data from the matrix to lists.

a.       On the graphing calculator, press the yellow 2nd key and then the x ö1 (x to the negative 1) key (MATRIX).  You should see a row x column size designation next to the matrix name that you choose.  As shown in the screen shot below, the carbon dioxide data stored in matrix A in the computer were sent to matrix A in the calculator.

 

b.      Go back to the Home Screen of the calculator by pressing the yellow 2nd key followed by the MODE key.  Then, press the yellow 2nd key followed by the STAT key.  This is the LIST menu.  Move to the right once with the blue right arrow key to access OPS.  Move down with the blue arrow key until you get to row A:Matr>list(  as in the figure below left.  Press ENTER to select this option and the command will be pasted to the home screen of the calculator.

 

 

c.       Press the yellow 2nd key and then the x ö1 (x to the negative 1)key (MATRIX).  The first column is the NAMES column.  Choose the name of the matrix that you used to store the data by highlighting the number of the matrix and then pressing ENTER.  To choose matrix A, press ENTER since the number 1 is highlighted or press the number 1 on the calculator.  If you press the number of the matrix, do not also press ENTER.  Next, press the comma key (above the number 7).  Select the lists where the two columns of data should be sent.  Press the yellow 2nd key followed by the number 1 for L1.  Press the comma key (above the number 7) and then press the yellow 2nd key followed by the number 2 for L2.  Press the right parenthesis key (above the number 9) and then press ENTER.

    

 

d.      Press the STAT key (near the blue left arrow key) and then press the number 1 or ENTER for Edit.  The data in L1 are the years and the data in L2 are the CO2 (ppm) in the atmosphere.


 

Analyzing the Data with a Graphing Calculator:

 

Creating a Scatter-plot with the TI-83+ Calculator ö

Carbon Dioxide Concentration in the Atmosphere

 

            The data given below, Atmospheric Concentrations of Carbon Dioxide, were found at the web site http://exploringdata.cqu.edu.au/datasets.htm (CD)

The web site referenced Worldwatch Institute - http://www.worldwatch.org                                                     

 

Use the data to create a scatter-plot.  Describe the shape of the graph and predict the amount of carbon dioxide (in parts per million) in the atmosphere for the years 1996 ö 2001.  When did the carbon dioxide in the atmosphere increase at the greatest rate?


 

 

 

 

 

 

 

 

 


 

 

Before entering data in the calculator, clear data from lists L1 ö L6 in the data entry location. To do this, press the STAT key on the calculator followed by ENTER.  This chooses #1, Edit, since that number is highlighted.  You may also press the number 1 key.  Move up with the blue up arrow key and highlight the name of a list that contains data.  Press the CLEAR key (found below the blue down arrow key) and then press ENTER.  These three steps ö highlighting the name of the list, pressing CLEAR, and then pressing ENTER ö will clear data from a list.  Follow these steps for each list that contains data.  (Note:  There are other ways to clear data from lists, but this method works well with students.)

 

 

Enter the years in List 1 and the amount of carbon dioxide (parts per million) in List 2.  Note:  Do not highlight the name of the list to enter data.

 

            Press the Y= key (the top key on the left column of the calculator) and clear out any equations that were entered in this location.  The CLEAR key is near the top of the right column of keys on the calculator.  Then, press the 2nd key (the yellow key on the ö83 and ö83+ calculators) followed by the Y= key.  This gives the STAT PLOTS menu.

 

 

Press ENTER or press the number 1 key to access the set-up for the first STAT PLOT.  Then, press ENTER to turn the plot on.  Move down to the Type line by pressing the blue down arrow key and press ENTER on the first type (Scatter-plot).  Move down to the Xlist and put the list name for the independent variable.  Using the year as the independent variable, L1 should be entered here.  To access the list name L1, press the 2nd key followed by the number 1 key.  Move down to the Ylist and press the 2nd key followed by the number 2 key.  The list names L1 ö L6 are the 2nd shift of the keys 1 ö 6.  Press ENTER on the largest Mark on the last row of the screen.  See the screen shot below.

 

Now, press the Y= key.  Plot 1 should be shaded.  You have made this plot active ö it will graph the chosen lists.  If Plot 2 or Plot 3 is shaded, you need to de-activate these plots.  To turn them off, move up with the blue up arrow key and ãblinkä on the plot name.  Press ENTER and move down with the down arrow key.  The plot name should no longer be shaded.

 

 

 Choose a window appropriate for these data by pressing the WINDOW key (top row of the calculator) and entering values.  A negative value was chosen for Ymin so the x-axis will show clearly.  The scale (Xscl and Yscl) controls the placement of ãticä marks on the axes.  Press the Graph key (top row of the calculator) and you should see a scatter-plot of the data.

 

 

Press the TRACE key (top row of the calculator) and you can trace on the data points.  Press the right arrow key to move to the other points.  If your screen doesnât show the axis, the plot information (P1:L1,L2), or the numbers at the bottom of the screen, hit the 2nd key followed by the ZOOM key (top row of the calculator) and press ENTER on each option in the first column.  These are the FORMAT options for graphing.

  

 

Pressing the ZOOM key and then the number 9 (ZoomStat) is a short-cut method for selecting a window that will display all data.  If you press WINDOW, you can see the values used for the graph with the ZOOM 9 option.

  

 

            Which graph gives a more realistic representation of the data?  Use the data set and one of the graphs to estimate the amount of carbon dioxide in the atmosphere in the year 2000.  Visit the Worldwatch Institute web site to confirm that estimate.  Use the data set or one of the graphs to predict the amount of carbon dioxide in the atmosphere in the years 2005 and 2010.

 


 

 

Graphing Change with the TI-83+ Calculator

 

            Use the carbon dioxide data to describe the changes in the carbon dioxide concentration in the atmosphere during different periods of time. To find the change in carbon dioxide concentration between each of the years given, highlight the name of List 3 (L3) and then press the 2nd key (yellow) followed by the STAT key.  Move to the right in the STAT menu with the right arrow key to the OPS column and press #7 (delta List).  Then press the 2nd key (yellow) followed by the number 2 key for L2.   Close the parentheses and then press ENTER.

 

 

            To graph the changes in population, return to L1 and delete the first entry in the list.  Now, you can graph L1 (the ending year of each time period given) as the independent variable and L3 (the change in carbon dioxide concentration in the atmosphere) as the dependent variable.  The data point (1791, 3) would give the change in carbon dioxide concentration from 1764 to 1791.  (A reminder:  To graph a scatter-plot, you must have the same number of entries in both lists.)

   

 

            After setting up a STAT PLOT for L1 and L3, press the ZOOM key followed by the number 9 key to choose a window appropriate for these data.  (See the screens above) Press TRACE and then the right arrow key to see the change in population during different 10-year periods.

  

 

Interpreting graphs of change is often difficult for students.  Between 1953 and 1959, the carbon dioxide concentration in the atmosphere increased by 3.1 ppm.  See the graph on the right above.  However, the ãdropä in the graph may suggest to some students that the carbon dioxide decreased rather than increased during this period.  Creating and interpreting graphs of change may be helpful in correcting such misconceptions and improving studentsâ graph interpretation skills.