In M&M Exponentials students will experiment with growth and decay functions. Students will also graph their experimental data and create theoretical equations for exponential growth and decay. In addition, students will use the theoretical equations to solve real-life problems.
Before the Activity
Experimental Steps for Students
- DO NOT EAT THE MANIPULATIVES!
- Start with a cup of 4 M&Ms.
- Shake the cup and pour the M&Ms out on the paper towel. Count the number of M&Ms that have the M showing. Add an M&M for each one with an M showing. Record the total number of M&Ms next to t=1.
- Repeat for 6 trials.
- Graph trials onto a scatter plot with trials on the x-axis and total M&Ms on the y-axis and predict a 10th trial.
During the Activity
Students use the TI-Nspire software to help them create a spreadsheet and investigate the impact of many trials. They use tools and formulas to to see the effect of exponential growth. In the process they use random generated values to simulate the M&M experiment.
After the Activity
Students are to discuss the following questions:
- What type of function is your scatter plot most alike? Linear? Quadratic? Exponential? Or Power? [It should model exponential functions.]
- What does the 10th trial produce? [Answers may vary but should be close to 4(1.5)^10. ]
- What does the input variable represent in terms of the M&M activity? [The input variable is the number of trials.]
- What does the output variable represent in terms of the M&M activity? [The output variable is the number of M&M's.]
- What is the y-intercept and how does it relate to the M&M's?
[You started with only 4 M&M's; it represents the number of M&M's when trials is 0.