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.

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