Exam 1
M464001
Fall, 2008
Name:
Part I.
Suppose that in a population of
N
animals we
have the following conditions (as represented in the dia
gram at right.)
•
Birth rate is
b
= 0
.
01
per month
per animal.
•
Death rate is
d
=
N
80000
per month
per animal.
•
h
= 3 animals are removed from the population in
each
two month
time period.
b
N
d
h
1. Write a difference equation for
N
.
2. Find all equilibrium solutions.
3. Sketch the equilibrium solution(s) on a time
N
graph. Be sure your graph is properly labeled.
4. On the same graph, sketch the graph of a population for which
N
(0) = 300 animals.
5. On the same graph, sketch the graph of a population for which
N
(0) = 700 animals.
1
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Part II.
Below there are three difference equation models.
There are also three population
graphs, each with
N
(0) = 1000. For each model, indicate which graph, if any, is a possible solution.
In the blank after each equation write the letter of the appropriate graph or “None”.
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 Fall '08
 DougBullock
 Math, Demography, Population Ecology

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