Group Names_________________________________________________________________
EXPONENTIAL GROWTH AND DECAY ACTIVITIES
OVERVIEW: You will conduct two simulations that result in
exponential functions. A simulation is a procedure for conducting an
experiment similar to a real-world situation. In this activity, you will
use Skittles as models to simulate population growth and isotropic
decay.
MATERIALS: You will need a bag of Skittles and a box.
PART I: AN EX-PLOSION of TRIBBLES
Introduction: Investigating the supposedly lifeless fourth planet in the Gamma Eridani system,
Kirk and Spock are surprised to find a previously unreported life from with an amazing
reproductive rate. These new life forms, called Tribbles, are small furry creatures with an “S”
shaped pattern on one side. Tribbles reproduce asexually (by themselves). Reproduction is
triggered when the side of the Tribble with the S pattern is exposed to light. Initially, only two
Tribbles were living and capable of actively reproducing.
Instructions: Place the first 2 Tribbles in the box, close the lid, and shake it a few times. Open
the lid; for every “S” that appears, add another Tribble (i.e., Skittle). Record the total number of
Tribbles now in the box (even if unchanged). This is the end of that shake (round). The number
of Tribbles present at the end of a shake is the total population at that time. Remember that at
shake 0, the number of Tribbles was 2. Record your data in the chart below for 10 rounds, then
proceed to page 2.
Note: Throughout the activity, make sure that each skittle has an “S” on it.
Round #
Population of Tribbles
0
2
1
2
3
4
5
6
7
8
9
10
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1. Using your own paper, neatly create a scatter – plot of your population data. Let the x-axis
represent the number of shakes and the y-axis represent the population. Label your graph
accordingly. Attach your graph to this activity.
2. Enter the data into your calculator and find an exponential equation that best fits this data;
also record the correlation coefficient, r.
y = _____________________________________________________________
r = _____________
3. What is the theoretical exponential equation for the Population of Tribbles? Why are their
differences between your equation and the theoretical equation?
4. Use this data to predict the population of Tribbles after ______ shakes.
Explain the general method used for determining your answer.
a) 20 shakes
population = _____________________________
b) 100 shakes
population = _____________________________
PART II: THE DECAY OF SKITTLEIUM ISOTOPES
Introduction: The decay of radioactive isotopes creates interesting data. The isotope Skittleium
is commonly found in vending machines throughout the world. The final decay elements of
Skittleium are Skittles. We will be measuring the decay of Skittleium.
Instructions: You need 100 isotopes of Skittleium to do this activity.
Place the isotopes in a box so that the “S” side is up. Cover the box with a
lid and shake it a few times. Take off the lid, and remove all the decayed
Skittles (decayed Skittles are the ones that do not have an “S” on top).
Count how many Skittleium isotopes are still in the box and record this
number in the table below. Dispose of decay elements. Replace the lid and
shake again. Remove the decayed Skittles, count and repeat until no
Skittles remain in the box or 10 rounds … whichever comes first.
Note: Throughout the activity, make sure that each skittle has an “S” on it.
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Round #
Number of Skittleium Isotopes Remaining
0
100
1
2
3
4
5
6
7
8
9
10
(Extend the table if needed)
1. Create a scatterplot of your Skittleium isotope data. Let the x-axis represent the number of
shakes and the y-axis represent the number of Skittleium isotopes. Label your graph accordingly.
Attach your graph to this activity.
2. Enter the data into your calculator and find an exponential equation that best fits this data;
also record the correlation coefficient, r. Note: For exponential equations, the y value cannot
equal zero; therefore, do not include this data point in the table.*
y = _____________________________________________________________
r = _____________
* Can you explain why the y-value in exponential equations cannot be zero?
3. What is the theoretical exponential equation for the decay of Skittleium isotopes? Why are
their differences between your equation and the theoretical equation?
4. Based on your findings above, approximately how many years would it take for 1000
Skittleium isotopes to decay? Explain the general method used for determining your answer.
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