# 3_1__Exponential_Growth_Decay_Activity

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```					ADV PRE CALC                                  NAME__________________________
Ch 3.1
EXPONENTIAL GROWTH
LAB ACTIVITY: PENNIES

MATERIALS: a cup of pennies

1. Put 2 pennies in a cup. (This is trial #0) Shake the cup. Dump out the pennies. See
how many heads you have. Add that number of pennies to the cup. Repeat for 11
trials.
Record the data in the chart below.

Trial       0       1      2     3       4      5   6     7     8      9     10       11
# of        2
pennies

2. Input the data into the graphing calculator
L1: trial Number        L2: # of pennies

3. Create a scatterplot of the data
2nd Stat Plot 1:
Xlist: L1
YList: L2
Hit Zoom 9

4. The graph is an exponential growth. Let’s find the equation using the calculator.
STAT CALC 0: ExpReg
ExpReg L1, L2, VARS Y-VARS enter enter enter
Your screen should show an equation y = abx
Where x = trial number
Write the equation you see:_______________________________
Hit zoom 9 to see the graph again

5. Use this equation to check on your observations

a. Trial x = 5       observed:_______________ model prediction:____________

b. Trial x = 9       observed:______________ model prediction: _____________

6. How many pennies does your model predict for trial 13? _________________
EXPONENTIAL DECAY                           NAME__________________________
ACTIVITY: M&M’S

MATERIALS: About 40+ M&M’s, paper cup, sheet of notebook paper

1. Count your M&M’s. Record this number as Trial #0

2. You are to dump all of your M&M’s into the cup.
Gently shake and dump contents of cup onto the notebook paper.
All M&M’s that land with the M showing are now to be destroyed ( um…wonder
how you should accomplish this task?) Count remaining M&M’s and record this
number under trial 2. Return these M&M’s to cup and repeat . Do this for 7 trials
or until you have “0” left.

Trial  0             1         2         3         4          5       6         7
Number
M&M’s
left

3.Enter the data into lists L1: trial Number   L2: M&M’s
4.Create a scatterplot of the data
2nd Stat Plot 1:
Xlist: L1
YList: L2
Hit Zoom 9

5. The graph you see is an exponential decay. Let’s let the calculator find the
equation using
STAT CALC 0: ExpReg
ExpReg L1, L2, VARS Y-VARS enter enter enter
Your screen should show an equation y = abx
Where x = trial number
Write the equation you see:_______________________________
Hit zoom 9 to see the graph again

6. Use this equation to check on your observations

a. Trial x = 3   observed:_______________ model prediction:____________

b. Trial x = 5   observed:______________ model prediction: _____________

b. Trial x = 7   observed:______________ model prediction
CLASS DATA

Exponential Growth

Trial       0      1        2   3       4       5   6       7       8   9   10       11
# of
pennies

EXPONENTIAL GROWTH EQUATION:

__________________________________________________________

EXPONENTIAL DECAY

Note:
Once a student has a “0” entry stop tabulating class data

TRIAL  0              1           2       3       4           5       6        7
NUMBER

M&M’S
LEFT

EXPONENTIAL DECAY EQUATION

________________________________________________________

```
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