Math 306 – Test 2 – Chapters 2 & 3
Printed Name:
• H
indicates a “By Hand” problem where technology is
not
allowed. One exception is the
Apart
command which may be used at any time.
•
T
indicates a “Technology” problem where you
::::
may use
Mathematica or a calculator. You
must still show the steps taken. For example,
Z
5
1
(1

x
)
7
dx
=

8
,
192 is valid. Giving
the answer

8
,
192 without the integral is not.
Please
put
your
name
on
computer
work
as
well
as
the
problem
number!
•
Do not use
DSolve
or
NDSolve
unless otherwise directed (except for checking your work).
Grade
of 100
H
1
10
pts
A tumor may be regarded as a population of multiplying cells. It is found empirically that the “birth rate”
of the cells in a tumor decreases exponentially with time, so that
β
(
t
) =
β
0
e

αt
where
α
and
β
0
are positive
constants, and hence
dP
dt
=
β
0
e

αt
P,
P
(0) =
P
0
.
Find the maximum tumor size.
2
Suppose that at time
t
= 0, 5 thousand people in a city have heard a certain rumor. Assume that time is
in weeks,
P
(
t
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 Spring '11
 KeithEmmert
 Math, ........., Elementary algebra, Complex number, Dr. Emmert

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