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Q
uantitative
R
easoning &
P
roblem
S
olving
432
© 2014 Pacific Crest
M
odel(s)
Exemplars and representations
L
imited
R
esources
Scenario/Experiment:
A single animal population exists in an isolated environment with a limited
supply of resources. The population at any given time is changing based on
the difference between new births and deaths. The birth rate is a constant so
the number of new births just depends on the current population. The death
rate is a combination of a constant (i.e. old age) and a function that depends
on the supply of resources.
-20
0
20
40
60
80
100
120
0
20
40
60
80
100
120
Population
Time
Figure 3
The birth rate is lower than the
constant death rate leading to extinction.
0
200
400
600
800
1000
1200
1400
0
20
40
60
80
100
120
Population
Time
Figure 2
The birth rate is between the constant death
rate (i.e., old age) and the combined death rate (i.e.,
old age and lack of resources) leading to a population
which oscillates around the resource supply (enough
resources for 1000 individuals was used here).
0
20000
40000
60000
80000
100000
120000
0
20
40
60
80
100
120
Population
Time
Figure 1
The birth rate
exceeds the combined
death rate leading to
exponential growth.