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Unformatted text preview: 1 Solutions and allowing
implies 15 gives the equilibrium solution. The initial condition
. Thus
. 28. Since
at
for all integers
we have equilibrium
, none of which satisfy the initial condition
.
lines at
Separating variables gives
and integrating gives
. We can solve for here using the initial condition: we get
Solving for gives
29. Separating variables gives
. Solving for gives
condition gives
. So
30. In standard form we get and integrating gives
, for
. The initial
.
so is an equilibrium solution.
. Integrating we get Separating variables gives
allowing . Solving for we get
gives the equilibrium solution. 31. We assume the decay model
bone then
. Thus
years , for . However, If is the age of the
. Solving for gives 32. Let
denote the number of Argon atoms in the sample. Then
is
the number of Potassium atoms. Let be the age of the rock. Then
years ago there were
atoms of Potassium . Hence
. On the other hand,
. This
and hence
million years
implies that
old.
33. We need only solve
years. for . We get 34. The ambient temperature is
F, the temperature of the ice water.
From Equation (12) we get
. At
we get
, so
and
. After
minutes we have
and solving for gives
. To ﬁnd the
time when
we solve
, with as above. We get
minutes.
35. The ambient temperature is
. Equation (12) gives
for the temperature of the coﬀee at time . Since the initial
temperature of the coﬀee is
we get
.
Thus
. The constant is determined from the temperature at a
second time:
so
. Thus ...
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.
 Fall '08
 BELL,D

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