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Math 227 Section 4 and 5
Worksheet on the Logistic Growth Model
Due March 21
Name
Instructions.
Write up your solutions using brief but complete English and algebraic sentences and appro
priate punctuation.
Poorly written work will not be graded.
Let
t
denote time and
P
(
t
)
the number of individuals in a population at time
t:
The logistic growth
model is based on the following di/erential equation:
dP
dt
=
kP
(1
±
P
B
)
where
k
and
B
are positive constants. It is assumed that initially,
0
< P < B:
When
P
is small, we have
dP
dt
²
kP;
so the constant
k
can be viewed as the instrinsic growth rate of the population. When
P
gets
large (but less than
B
)
, the factor
(1
±
P=B
)
diminishes the rate of growth. As you will see,
P
will never
reach or exceed
B:
The constant
B
is called the
carrying capacity
.
equation
P
B
±
P
=
Ce
kt
:
where
C
is a constant.
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 Spring '09
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 Calculus, Algebra

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