Dec.
13,
1996
MATH
115
FINAL
EXAM
INSTRUCTIONS:
Number
the
answer
sheets
from
1-10.
Write
your
name,
section
number,
and
TA's
name
on
each
answer
sheet.
Answer
each
numbered
problem
on
a
separate
answer
sheet.
Read
carefully,
mark
your
answers
clearly.
You
must
show
all
appropriate
work
in
order
to
receive
credit
for
an
answer.
If
a
problem
asks
for
an
exact
answer,
algebraic
methods
must
be
used
to
obtain
the
answer
(and
the
work
must
be
shown);
a
calculator
approximation
will
not
receive
credit
if
an
exact
answer
is
requested.
Good
luck!
Answer
Problem
1
on
Answer
Sheet
1.
(io,io)
1.
a.
Find
an
equation
for
the
line
through
the
points
(-10,
5)
and
(15,180)
b.
Use
a
table
of
signs
to
solve
the
inequality
(4
-
x)(x
2
+
4)(3x
+
7)(x
-
2)
2
>
0.
Answer Problem
2
on
Answer
Sheet
2.
2
X
+1
(6,6,6,6)
2.
Let
f(x)
=
g
_2
and
g(x)
=
In
(5
-
x)
a.
Find
(f
+
g)(x)
and
the
domain
of
f
+
g
b.
Find
(f
°f)(x).
Simplify
your
answer.
c.
Find
g'
l
(x).
d.
Find
h
^~
g(4)
.
Simplify
your
answer.
Answer
Problem
3
on
Answer
Sheet
3.
x
2
-4
(ins)
3.
a.
Let
f(x)
=
-^
r-
Find
each
of
the
following
for
the
graph
of
f.
Whenever
one
of
them
does
not
^rj\
I™
£
exist
write
NONE.
i.
x-inter
ept(s)
ii.
y-intercept
iii.
vertical
asymptote(s)
iv.
horizontal
asymptote
b.
Let
g(t)
=
3
sin
(TI
t
+
^
).
i.
Find
each
of
the
following
for
the
graph
of
g:
amplitude,
period
and
phase
shift
ii.
Use
an
identity
to
find
a
function
in
the
form
h(t)
=
a
sin
bt
or h(t)
=
a
cos
bt
so
that
g(t)
=
h(t).
Answer
Problem
4
on
Answer
Sheet
4.
25
a
2
do.io)
4.
a.
Find
log
a
g
using
the
values
Iog
a
5
=
.7325
andlog
a
2
=
.3155
b.
Solve
for
x
(exact
value):
2
2x
(8
x
-
4
)
=
16
3/2
Answer
Problem
5
on
Answer
Sheet
5.
(12)
5.
One
model
for
population
change
is
the
function
f(t)
=
A
e
kt
,
where
A
and
k
are
constants
and
t
is
the
time elapsed.
The
number
of
bacteria
in
a
colony
is
halved
every
5
hours
if
the
temperature
is
held
constant
at
a
low
temperature.
a.
Write
the
function
for
this
population change
if
the
initial
bacterial
count
is
2,000.
If
you
use
any
approximations,
use
at
least
four-place
accuracy.
b.
How
long
will
it
take
for
the
population
to
reach
a
count
of
200
(to
the
nearest
tenth
of
an
hour)?
Please
turn over
for
Problems
6-10.
I
of
2
