Double Your Pleasure

Name _______________________________                                           Date ________

Math Concepts:     Exploring exponential functions.
                           Data collection and analysis.

Materials :     TI-83 Plus Calculator
                       M & M candies  -  75 candies per person
                     Paper Cup
                       Paper Towel

Overview :  This activity focuses on the collection of data.  Analyze it to find the
                     relationship between the “year” number and the “population” of candies.

Collecting the Data :    

Start with 4 M&M’s in your paper cup.  This will be considered “year zero” in your experiment.  Pour the M&M’s on to your paper towel and then add twice the number of M’s that are facing up.  This new total will be considered “year one” in your experiment.  Pour out the M&M’s again on to your paper towel and repeat the process again and again until you reach year five or you run out of M&M’s.  Record the population of M&M’s for each year into the table.


Year

Population

0

 

1

 

2

 

3

 

4

 

5

 

Analyzing the Data:

  1. Enter the data from your table into lists L1 and L2 on your calculator.
  2. Turn on Stat Plot 1 with non-connected points type selected.
  3. Set an appropriate window for your data.
  4. Plot your data on the screen of your calculator.

5.  Use Stat Calc to fit a LinReg equation to your points.  Write your linear
     equation and the correlation coefficient.   

       Linear equation :            y  =  ____________________

      Correlation coefficient :  r  =  ____________________

      Enter your linear equation into “ y1  =”  and look at the graph. 

       Does it appear that your data points are linear?       __________

  1. Look at the following table of sample data from a previous experiment in

        which three people combined their results.
     


Year

Population

0

12

1

25

2

49

3

95

      If you tried to fit an exponential function to this data, you might look at the
       data and conclude that:
                                          12  =  12  *  20
                                          25  ≈  12  *  21
                                                            49  ≈  12  *  22 
                                          95  ≈  12  *  23
                                             .         .       .
                                                         .         .       .    
                                          y   ≈   12 *  2x

      7.  Try to find an exponential function for your data.  Enter this function into “y2 =
           on your calculator and see how well it fits the data points.  Write your equation
           here:    
                                    y  =  ____________________

  1. Use  Stat Calc on your calculator to fit an ExpReg equation to your data points. Write your exponential regression equation and the correlation coefficient.        

        Exponential regression equation :            y  =  ____________________

      Correlation coefficient :                             r  =  ____________________

               Enter this equation into “ y3  =”  and look at the graph. 

9.   Using this equation predict the population of  M&M’s for years 6, 7, and 8 in
      the table below:
                       
                       


Year

Population

6

 

7

 

8

 
    1.   Make a new table using the total results from all the students in the class.

Year

Population

0

 

1

 

2

 

3

 

4

 

5

 
    1.  Using this table repeat steps 1 through 4 from page 1.
    2.  Use  Stat Calc on your calculator to fit an ExpReg equation to your data

               points.  Write your exponential regression equation and the correlation
               coefficient.         

         Exponential regression equation :            y  =  ____________________

       Correlation Coefficient :                             r  =  ____________________

               Enter this equation into “ y1  =”  and look at the graph. 

  1.   Using this equation predict the population of  M&M’s after years 6,  7, and  8

         in the table below:
                     


Year

Population

6

 

7

 

8

 

   14.  Write a few sentences comparing your experimental results equation (what you got) with

          the theoretical results equation (what should happen).

Ray Weier