MATH 106D - CALCULUS II
WINTER 2005
QUIZ 10
NAME:
Show ALL your work CAREFULLY.
Rabbits were brought to a remote deserted island some years ago. The
growth of the rabbit population is governed by the following logistic differ-
ential equation.
dR
dt =0.1R(1000 −R)
Here, R=R(t) denotes the population of rabbits at time t.
(i) What will the rabbit population be in the long run? (What is the
equilibrium solution?)
Now, suppose bobcats were later brought to this island and a population
model for the rabbits and for the bobcats is given by the following system.
dR
dt =R2−R−
B
3
dB
dt =B1−R−
B
2
where Band Rdenote the population of the bobcats and of the rabbits (at
time t) respectively.
Date: April 8, 2005.
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