Pop & Ag #___
Modeling Population Growth
Integrated Science 3
9/15
Name:
Per.
 Background
Probably the most significant factor behind any current resource/environmental issue is the
phenomenon of exponential growth. Over the past few decades, human population, non-renewable
resource consumption, food production, industrial output and pollution have all been increasing
exponentially. To understand population dynamics, one must understand exponential growth. This lab is
designed to give you that understanding. It is built around human population growth, but it could just as
well be applied to any population in any ecosystem.
 Procedure
1. In this experiment you will use dice to model population growth.
2. You will conduct three simulations: a) high birth rate; b) reduced birth rate; and c) increased death rate.
You will follow slightly modified directions for each simulation.
3. Record data in the provided data tables. Construct the requested graphs for your data analysis.
Simulation A: High Birth Rate
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General Rules
Each throw represents one year
Each die represents the reproductive activity of 5 people while the population is under 250 people
Each die represents the reproductive activity of 10 people when the population is over 250 people
Simulation A Rules
Quick Key
Throws of 1 or 2 represent live births
 1, 2  births
Throws of 3 represent deaths
 3  death
Throws of 4, 5, or 6 represent neither births nor deaths
 4, 5, 6  nothing
1.
2.
3.
4.
5.
The first 14 years of data have been collected for you and are recorded in Data Table A.
Begin this simulation at year 15 with a population of 115 people.
Put 23 dice to represent that population into the container.
Each of the dice represents the reproductive activity of 5 people during one year.
Roll the dice. Count all of the dice that represent a death. Remove those dice from your population and
record the number of deaths in Data Table A.
6. Count all the dice that represent live births. Record the number of births in the Data Table A. Add
another die to your population to represent the births of every 5 individuals.
7. Continue to roll the dice. Once your population exceeds 250 people, assign each die a value of 10
people. Repeat these procedures until the total population exceeds 500 people.
Simulation B: The Effect of Decreasing Birth Rate
1. Begin this simulation at year 15 with a population of 115 people.
2. Put 23 dice to represent that population into the container. (Recall: 1 die = 5 people)
3. Simulation B will have the following modification: only a roll of 1 represents a live birth.
Simulation B Rules
Quick Key
 Throws of 1 represent live births
 1  births
 Throws of 3 represent deaths
 3  death
 Throws of 2, 4, 5, or 6 represent neither births nor deaths  2, 4, 5, 6  nothing
4. Roll the dice. Count all of the dice that represent a death. Remove those dice from your population and
record the number of deaths in Data Table B.
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5. Count all the dice that represent live births. Record the number of births in the Data Table B. Add
another die to your population for each birth.
6. Repeat this simulation model for 10 throws of the dice. Once your population exceeds the 50 dice you
have, assign each die a value of 5 people. Once your population exceeds 250 people, assign each die a
value of 10 people.
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Simulation C: The Effect of Increasing the Death Rate
1. Begin this simulation with year 15 with a population of 115 people
2. Put 23 dice to represent that population into the container. (recall: 1 die = 5 people)
3. Simulation C will have the following modification: rolls of both (2) and (3) represent a death.
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Simulation C Rules
Throws of 1 represent live births
Throws of 2 or 3 represent deaths
Throws of 4, 5, or 6 represent neither births nor deaths
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Quick Key
1  births
2, 3  death
4, 5, 6  nothing
4. Roll the dice. Count all of the dice that represent a death. Remove those dice from your population and
record the number of deaths in Data Table C.
5. Count all the dice that represent live births. Record the number of births in the Data Table C. Add
another die to your population for each birth.
6. Repeat this simulation model for 10 throws of the dice. If your population declines to fewer than 50
people, make each die represents one person.
 Data Tables - See next page
 Calculations: SHOW ALL WORK.
In the table below, calculate the population growth rate for the final 10 years (throws) of each simulation (A,
B and C). Use the equations below. Show how you set up each formula and box your final answers.
Sim.
Growth rate (r) for final 10 years (throws)
according to equation below
Doubling time for final 10 years (throws)
according to equation (in years)
A
B
C
KEY
𝑟 =
(𝑃𝑛 − 𝑃0 )
1
×
𝑃0
𝑛
doubling time =
70
r
r = growth rate
n = number of years in time period
Pn = final pop in time period
Po = starting pop in time period
 Graph - Be sure to check for title, labeled axes and provide a key.
Use your data to construct a graph representing “The Effect of Time on Population Growth for Simulation
A, B and C.” Make sure to include a Key to distinguish the three different simulations.
 Analysis and Conclusion – Answer these questions on a separate sheet using complete sentences.
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1. Based on the data, describe what happened to the population growth in each simulation. Be sure to refer
to your graph and use specific data to support your conclusions.
2. Based on the data, explain why you got the results you did. What specific ‘real-life’ factors that might
contribute to the changes in birth rate and death rate that occurred in Simulations B and C.
3. Identify which of the simulations most closely resembles real data on human population growth.
 Data Tables
Data Table A:
High Birth Rate (Sim. A)
Throw
#
1(Years)
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
# of
Births
4
4
3
2
8
5
7
6
10
11
16
16
31
40
# of
Deaths
1
1
3
2
3
4
4
2
5
3
9
6
0
15
New
Pop.
13Size
16
16
16
21
22
25
29
34
42
49
59
90
115
Data Table B:
Reduced Birth Rate (Sim. B)
Throw #
(Years)
# of
Births
# of
Deaths
15
16
17
18
19
20
21
22
23
24
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New
Pop.
Size
Data Table C:
Increased Death Rate (Sim. C)
Throw #
(Years)
15
16
17
18
19
20
21
22
23
24
# of
Births
# of
Deaths
New
Pop.
Size
37
38
39
40
41
(You may not need all the rows available)
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