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 TowelOverview : 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:
- Enter the data from your table into lists L1 and L2 on your calculator.
- Turn on Stat Plot 1 with non-connected points type selected.
- Set an appropriate window for your data.
- 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? __________
- 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 * 2x7. 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 = ____________________
- 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 |
Year |
Population |
0 |
|
1 |
|
2 |
|
3 |
|
4 |
|
5 |
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.
- 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