Name__________________________
Partner(s)___________________________ __________________________
M & M Lab (Exponential Growth and Decay)
Part 1: Exponential Decay
1) Count the total number of M&Ms you have in your cup. Record this number in
trial #0.
2) Put all the M&Ms in your cup. Pour them all out onto your plate.
3) Remove all the M&Ms that come to rest in the shaded sector of your plate.
4) Continue this process and record each trial in table 1. You are done when you
have completed 10 trials –OR- when your M&M population gets below 4. Do NOT
record 0 as the population.
Table 1
5) Also, record the percent of M&Ms you remove in each trial in table below.
Table 2
Calculate the average of all the percentages in the table above:________________. This value is r, the rate of decay.
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6) Describe the relationship that exists between 𝒙 and 𝒚 (table 1):
 As the value of 𝒙 increases, the value of 𝒚 ______________.
 This rate of ______________ [increase/decrease] becomes
__________ [greater/less] as values of 𝒙 increase.
7) Record your data from Table 1 in a scatter plot on the axes below.
8) We can write an exponential decay function that models the data above using
the formula:
𝒚 = 𝒂𝒃𝒙
𝑎 = initial number of M&Ms
𝑏 = 1-r
(r=decay rate, the average
percent from table 2)
𝑥 = trial #
9) What is the value of a in your experiment? _______________________
10) What is the value of b in your experiment? _______________________
11) Based on these values, what is the decay function for your M&Ms
experiment?
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12) Use your decay function from #11 above to determine your M&M population
on the 4th trial.
𝑦 =__________
How does this number compare to your
actual data for trial #4 in table 1? ____________ Are they the same?
___________
What are some reasons why your results are different?
Part 2: Exponential Growth
1) Place 4 M&Ms in your cup. This is trial #0. Record it in your table
below.
2) Shake the cup and dump out the M&Ms on the plate. For every
M&M with the “M” showing, add one M&M. Record the new total of
M&Ms for trial in table 3 for trial #1. (EX: If 2 M&Ms land with the
“M” up, add 2 more M&Ms.)
3) Repeat step 2 until you have done 10 trials –OR- you run out of
M&Ms.
Table 3
4) For each trial, also record the percentage of M&Ms that landed
with the “M” up in table 4.
Table 4
Calculate the average of all the percentages in the table above:________________. This value is r, the rate of growth.
3
5) Describe the relationship that exists between 𝒙 and 𝒚 (table 3):
 As the value of 𝒙 increases, the value of 𝒚 ______________.
 This rate of ______________ [increase/decrease] becomes
__________ [greater/less] as values of 𝒙 increase.
6) Record your data from table 3 in a scatter plot on the axes below.
7) We can write an exponential growth function that models the data above
using the formula:
𝒚 = 𝒂𝒃𝒙
𝑎 = initial number of M&Ms
𝑏 = 1+r (r=the growth rate, the average
percent from table 4)
𝑥 = trial #
8) What is the value of a in your experiment? _______________________
9) What is the value of b in your experiment? _______________________
10) Based on these values, what is the growth function for your M&Ms
experiment?
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11) Use your growth function from above to calculate trial #7. ______ How
does this compare with your actual data for trial #7 from table 3? ________
Explain why you think the two are different.
12) Use your growth function to predict the number of M&Ms there would be in
Trial 25___________
Trial 50___________
Part 3: Lab Discussion
1) In Part 1, what was the “a” value in your decay equation?________
In part 2, what was the “a” value in your growth equation?_________
What do the “a” values represent in your equations?______________
_____________________________________________________
Why were the “a” values different in parts 1 and 2 above?
_____________________________________________________
In general, what does the “a” value represent in the equation = 𝑎𝑏 𝑥 ?
Be specific! ____________________________________________
(For #2 below, remember 𝑏 = 1 ± 𝑟 )
2) In part 1, what was the “b” value in your decay equation?_______
In part 2, what was the “b” value in your growth equation?_________
What do the “b” values represent in your equations?______________
_____________________________________________________
Why were the “b” values different in parts 1 and 2?
_____________________________________________________
3) In the instructions for Part 1 (decay M&M lab), why do you think
you are NOT supposed to reduce the number M&Ms all the way to
zero? Explain.
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