Calculus II Midterm 2
March, 2009
2
1. (3 marks each; total 9 marks)
Answer each question in the space provided.
You
MUST show your work.
a)
Mad scientists colonize an empty island with 10 gremlins. The rate of growth of
the population can be modeled by the differential equation
P
dt
dP
7
=
. Find the
population of gremlins as a function of time.
b)
If
t
e
x
=
and
3
ln
t
t
y
−
=
, find
dx
dy
when
5
=
t
.
c)
Use Euler’s Method to approximate
)
4
.
1
(
y
with step size
2
.
0
=
h
for the
following initial value problem:
,
'
xy
x
y
−
=
0
)
1
(
=
y

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