MATH 127 FINAL EXAM 20 December 2004 SPECIAL CODE: 441220 p. 1 of 7
NAME (print):
__________________________________________________
SIGNATURE: ___________________________________________________
8 DIGIT
SPIRE ID #: ____ ____ ____ ____ ____ ____ ____ ____
CIRCLE the
name of your instructor below:
Rudvalis
Sect. 1
MWF 9:05
DIRECTIONS: This is a 120
minute exam. It consists of 25 multiple choice questions.
All your responses must be
recorded on the green
"bubble" sheets using a No. 2 pencil.
You are allowed to use any kind of calculator for this exam. You are responsible for having a
working calculator and knowing how to use it and also for having at
least one No. 2 pencil.
YOU MAY NOT SHARE A CALCULATOR WITH ANOTHER STUDENT DURING THIS EXAM.
You may use a two-sided 8.5
x 11 page as a review sheet during
the exam. If you need more
paper
raise your hand and we will supply you with scratch paper.
You may not have anything else on your desk except your STUDENT ID which
may be checked
during the exam and WILL BE CHECKED when you hand in your exam.
Before starting the exam you MUST DO THE FOLLOWING on your green
"bubble" sheet:
¡¤
WRITE your name at the top left side in the section labeled NAME and BUBBLE it below that.
¡¤
WRITE your 8 digit SPIRE ID in the section labeled
IDENTIFICATION NUMBER in the
middle of the bottom left
and BUBBLE it in below that using the spaces labeled A through H.
¡¤
WRITE and BUBBLE the SPECIAL CODE for this exam (441220) in the section with
that label.
¡¤
BUBBLE in your section number (1, 2, 3 or 4) in the column labeled GRADE or
EDUC.
¡¤
DO NOT write or "bubble" in the sections for SEX or BIRTH DATE. (-1 pts each if you do.)
¡¤
Your response to each of the 20 questions must be made by filling in the
appropriate bubble on
your answer
sheet. In GRADING your exam the
grading machine reads only the bubbles you
have filled out so entering
these bubbles correctly is vital to correctly recording your performance.
¡¤ All
bubbles must be filled in SOLIDLY using a #2 pencil.
¡¤
DO NOT LEAVE YOUR SEAT once you have started the exam until you are ready to
turn it in.
If you have a question or
need extra paper raise your hand and we will come to you.
¡¤ When
you have FINISHED, you MUST turn in the green "bubble" sheet AND this
COVER PAGE
of the test booklet and take
the test booklet with you. BEFORE
you turn in the cover page and
bubble sheet mark your answers
in the test booklet so you can figure out your score as the correct
answers will be put online after the
exam. Grades may NOT be posted on
OWL as our OWL
administrator will be out of the
country right after the final. Do
not call the department or your
instructor for grades as no grades
will be given over the phone. You
may try to e-mail your
your instructor for grades if you
cannot wait for them to be posted on SPIRE. BEST OF LUCK!
MATH 127 FINAL EXAM 20 December 2004 SPECIAL CODE: 441220 p. 2
of 7
1.
The number of
entering students at a university over the last four years is
given in the following
table.
year |
2001 |
2002 |
2003 |
2004 |
students |
920 |
1034 |
1220 |
1130 |
The average rate of change in the number of entering students from 2001
to 2004 was:
a)
210 students
b)
70 students
c)
70 students per year
d)
52.5 students
e)
52.5 students per year
2. A factory that produces radios has fixed costs of
$30,000 and variable costs of $20
per radio. If each radio can be sold for $24, how
many does the factory need to make
to break even?
a) 7500
b) 6000
c) 3000
d) 1500
e) 1250
3. Solve the equation: 2-7x = 12. The solution is:
a) -ln(12)/7
b) -ln(12)/7ln(2)
c) −[]/7ln(2)
d) -12/7ln(2)
e) −6/7
4. In
1994 the population of the
world was 5.6 billion people and was growing exponentially with growth rate
approximately 1.2% per year. Assuming this trend continues
indefinitely into the future, the doubling time (in years) is closest to:
a) 168
b)
58
c)
11
d) 9
e) 6
5. A radioactive substance decays
exponentially so the amount at time
t is S(t) = S0 e−rt,
where S0 is the initial amount.
Suppose the half-life is 25
years. Then the decay rate r
is
closest to:
a) 0.028
b) 0.5
c) 12.5
d) 0.125
e) 0.08
MATH 127 FINAL EXAM 20 December 2004 SPECIAL CODE: 441220 p. 3 of 7
6.
If y= f(x) = x53x, then y¡ä =
f¡ä(x) is:
a) 5x4 3x b) 5ln(3) x43x c) 5x5 3x-1
d) 5x43x + x53xln(3)
e) 5x43x + x52x
7. Let y = f(x) = x5 − 5x
with 0 £ x £ 2.
If A is the global maximum value of y
and
B is the global minimum value of y, then:
a) A = 4 and B = 0
b) A = 75 and B = −5 c) A = 22 and B = 4
d) A = 4 and B = −27 e) A = 22 and B = −4
8.
The circulation time (i.e. the average time required for all the blood
in the body
to circulate once and return to the heart) for
mammals at rest is experimentally
found to be PROPORTIONAL to the fourth root (i.e.
the ¼-th power) of the body mass.
If an elephant with body mass 5000 kg has a circulation time of 144
seconds then the
circulation time (in seconds) for a human being with
body mass 70 kg is closest to:
a) 120
b)
100
c)
70
d)
50
e) 20
9.
If y = f(x) = x3 - 4x2 + 7x - 11 then the SLOPE of the tangent
line to the
graph of
y = f(x) at x = -1 is:
a) 18
b) 6
c) -4
d) −12 e) −23
10. The derivative of (1+ln x)³ is:
a) (1 +
1/x)³ b)
(ln 3)(1+ln x)³(1/x) c) 3(1+ln x)²(1/x)
d) 3(1+ln x)² e)
3(1+1/x)²
11. At x=2, the function f(x)=ex/x
a) is increasing b) is
decreasing c) has a
local maximum
d) has a local minimum e) has an
inflection point
MATH 127 FINAL EXAM 20 December 2004 SPECIAL CODE: 441220 p. 4 of 7
12. Suppose y = f(x) is a continuous function for which f ¡ä(x) > 0
for x < 3, f¡ä(3) = 0 and f ¡ä(x) < 0 for x > 3. Which of the following MUST be true for
any such function.
a) The graph of y = f(x) has a local maximum at x = 3
b) The graph of y = f(x) has a
global minimum at x = 3
c) The graph of y = f(x) has an inflection point at x = 3
d) The graph of y = f(x) has a local minimum at x = 3
e) The graph of y = f(x) has a
global maximum at x = 3
13. For the function y = f(t) = te-3t find the value of t where the
graph of the function
has
an inflection point.
a) 1/3
b)
2/3
c) 1
d)
3/2
e) 2
14. Suppose the concentration C
of a drug is given by C(t) =
13.2t e-0.4t where
time t
is measured in hours and the concentration is measured in ng/ml.
The
time required to reach peak (i.e. maximum concentration is closest to:
a) 12
b) 6.0
c)
5.0
d) 2.5
e) 0.4.
15. The peak (i.e.
maximum)concentration in the problem above is closest to:
a) 4.86
b)
6.07
c)
8.10
d)
12.14
e) 30.35
16. A rumor spreads among a group of
800 people in a manner such that the
number
N(t) of people who have heard the rumor t hours after
it started to
spread is given by the function
N(t) = 800/[1 + 399e-0.3t].
The earliest time (in hours) at which half the people have heard the rumor is closest to:
a) 400
b)
20
c)
18
d) 7
e) 5
MATH 127 FINAL EXAM 20 December 2004 SPECIAL CODE: 441220 p. 5 of 7
17. Given that the area of the
shaded
region
in the figure at the right is
A,
Insert
Andrea's graph here
2
the
value of the integral ¨°-1 f(x) dx is:
a) 3A b) 2A c) A d) 0 e) -A
18. The graphs of y = x + 1
and y = x3 + 1 intersect at exactly 3 points and
thus
bound
two finite regions in the (x,y)-plane. The total AREA of these two regions is:
a) 0
b) 1/4
c)
1/2
d) 1
e) 2
19. Suppose an auto drives along a
straight
flat East-West road in a way
so
that its velocity is positive when it
Insert
Tim's graph here
is
moving Westbound and negative
when
it is moving Eastbound. The
velocity
of the auto is given by the
graph
at the right.
At
the end of three hours the distance (in miles) from its starting point is
closest to:
a) 27.75 b) 25.25 c) 22.5 d) 18.75
e) 15.0
20.
For the same auto as in the previous problem the total distance traveled
by the auto
(i.e. the change in the odometer reading) at the end
of the three hour trip is closest to:
a)
60 miles b) 72.25 miles
c) 81.25 miles
d) 85.5 miles
e) 90 miles
MATH 127 FINAL EXAM 20 December 2004 SPECIAL CODE: 441220 p. 6 of 7
21. Suppose y = f(x) is a continuous
increasing function y = f(x) and some of its values
are
given by the following table:
x |
0 |
0.5 |
1 |
1.5 |
2 |
2.5 |
3 |
f(x) |
3 |
5 |
8 |
11 |
15 |
19 |
21 |
Then a ¡°good approximation¡± for the total change of y = f(x) on the interval [0, 3]
obtained by averaging the ¡°left sum¡± and ¡°right sum¡± is closest to:
a) 140
b)
70
c)
63
d)
54
e) 35
22. Suppose that a function f(x) satisfies f(0) = 20 and f
¢(x) = 2x-4. Then
f(4) is closest to:
a) 36 b) 24
c) 20
d) 16
e) 4
23. The velocity of a car (in feet per second) is given
by the function v(t) = 4+3t-t²,
for t between 0 and 4 seconds. Since v(t) = 4+3t-t² = (1+t)(4-t),
v(t) is non-negative
throughout the interval [0, 4]. The total distance (in feet) traveled by the car in these
4 seconds is closest to:
a) 25
b)
20
c)
18.66
d)
18
e) 16
24. Using the same velocity
function as in the previous problem, what is the
maximum
velocity (in ft/sec) attained by the car during 0 £ t £ 4.
a) 6.5
b)
6.25
c) 6
d) 4
e)
1.5
MATH 127 FINAL EXAM 20 December 2004 SPECIAL CODE: 441220 p. 7 of 7
25. The graph below represents the velocity v(t) of a
model rocket t seconds after
launch, in feet per second. As usual velocity is positive while the
rocket is ascending
and negative while it is
descending. At time t = 0 the rocket has at altitude 0
(i.e. it is on the ground).
What is the approximate altitude
(in feet) of the rocket at time t
= 8 seconds?
a) 40 b) 55
c)
70
d) 100
e) 145