1
MATH 140B
QUIZ#11
Date: Dec 3, 2007
[ 2 ]
1.
A population of pheasants is introduced on an island. Lacking any natural predators, the
population flourished to 560 three years later. Assume that the population grows according
to the Malthusian model for population growth. That is, if
P
(
t
) denote the population at
time
t
, and
P
0
is the intial population, then
dP
dt
=
k
·
P
P
(0) =
P
0
.
where
k
is a positive constant of proportionality. Find the value of
k,
and use it to determine
the generation (doubling) time in years. Round your answer to the nearest decimal.
A)
1
B)
1.2
C)
1.4
D)
1.6
E)
None of the above
[ 2 ]
2.
The
BeerLambert Law
says that the intensity,
I
(
x
)
,
of light at depth
x
meters in seawater
is given by the decaying exponential function
I
(
x
) =
I
0
·
a
x
where 0
< a <
1 is a constant, and
I
0
is the intensity of light at the surface. The
photic zone
is the depth where the intensity of light is 1% of what is it at the surface. In Cape Cod, MA
the photic zone occurs at 16 meters. Find the value of the base
a.
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 Fall '07
 FABBRI,MARC
 Math, Exponential Function, Radioactive Decay, Light, Mathematical constant, photic zone, dP =k·P dt

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