Final Exam, Math 16B, Summer 2009
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) (12 points) Read carefully 
The famous “LotkaVolterra” equations for modeling predator/prey relationships are given by:
dx
dt
=
x
(
α
−
β
y
)
=
x
−
xy
dy
dt
=
−
y
(
γ
−
δ
x
)
=
xy
−
y
where
,
,
,
are constants,
x represents the size of population of the prey
,
y represents
the size of the population of predators,
and t is time [unitless].
(a) Below are four English descriptions of the four parameters
,
,
,
.
Please match the
parameter with its description.
______Population growth constant for predators
______Predation rate [predators on prey]
______Population growth constant for prey
______ Rate of natural death of predators
(b) What are some reallife parameters that impact predator/prey relations that are not captured
by this model? [in other words, what assumptions do you make by using this model]
(c) Below is a graph showing the size of predator and prey populations over time. Explain what’s
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 Fall '06
 Sarason
 Math, Calculus, Morphine, Dice

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