Prelim 1
Math 2930
Spring 2011
show work, 5 problems, no calculators
1 a)
(4 points)
Write your name and section number on your exam booklet.
b)
(12 points)
A glass of water at 28 degrees
C
is placed into a freezer at

18
C
. The water temperature
T
(
t
) obeys Newton’s law of cooling until it
reaches 2
C
. How long does that take, if we know that it gets to 20
C
in 15
minutes?
c)
(4 points)
Solve (3

5
i
)
c
=
i
+ 1 for the complex number
c
in the form
of
c
= (real) +
i
(real).
2 a)
(10 points)
A certain radioactive material decays with a halflife of less
than 30 years. We start with a mass
y
(0) = 1 gram of the material, and
y
(
t
)
is the remaining mass after
t
years. Explain whether
y
(300) is more, or less,
than 0
.
001 gram.
b)
(10 points)
Solve
x
0
+
(
1 +
1
t
)
x
= 0 with
x
(2) = 3, and state the interval
of
t
values in which your solution is deﬁned.
3)
(4 points for each part)
a) Find a solution to
y
00
=

2
y
with
y
(0) = 0 and
y
0
(0) = 5.
b) Check your answer to part (a) by substitution.
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 Spring '07
 TERRELL,R
 Math, Differential Equations, Equations, Radioactive Decay, HalfLife, Complex number, radioactive material decays

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