DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF MASSACHUSETTS

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

Nahmod Sect. 2 TuTh 9:30 Cook Sect. 3 TuTh 11:15 Braden Sect. 3 TuTh 1:00

DIRECTIONS: This is a 120 minute exam. It consists of 25 multiple choice questions.

Make sure you have all 7 pages and all 25 problems.

Your (percentage) score on this exam is 4 times the number of correct responses.

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) = x⁵3^x, then y′ = f′(x) is:

a) 5x⁴ 3^x b) 5ln(3) x⁴3^x c) 5x⁵ 3^x-1

d) 5x⁴3^x + x⁵3^xln(3) e) 5x⁴3^x + x⁵2^x

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)=e^x/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 ′(x) > 0 for x < 3, f′(3) = 0 and f ′(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 ò_-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