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Unformatted text preview: Fall 2007 Notes: Pledge (Sign your name) qerhrvpaosr.» {43
Math 151 Test 2A Name vi I...”
“w . DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO START. / Before you begin, write your name at the top of the page.
To receive partial credit for a problem, you must clearly show ALL WORK
All answers are to be completely simpliﬁed unless told otherwise. Do not ask the instructor how to do a problem; only ask about its legibility.
You may use the back of these pages as scrap paper. Don’t forget to check your work for errors before you submit your test. All functions must be cleared from your calculator before you leave the room.
Failure to do so constitutes an honor violation. Random checks will be
performed by your instructor. This test is worth 150 points. The weight of each problem is indicated by a
number within the set of parentheses; i.e. l. (20) means problem 1 is worth 20
points. This test is to be completed in one hour and ﬁfteen minutes. On my honor, I have cleared all functions from my calculator and have neither
given nor received help on this test. l. (5) Let an be the leading coefficient. Write the complete factored form of a polynomial with real coefﬁcients that satisﬁes the following conditions:
Degree = 3, an : —4 and zeros are —2, z' . ¥ (may): L)(x+i) 2. (5) Find the complete factored form of the polynomial, given that x = 3 and x = 4 are zeros.
f(x) = x4 ——x3 —25x2 +37x+60 (xsXxﬂ 1: xL—Ox H7—
3 '3 6x
xzOx Hz x"_x3z§x'+37x +4.0  (14415 #sz2 2 3  37 ‘+37x
x +OX+5 3 __ _ Efzxﬂzf qzx)
= (“SYX‘H 5x1 3$'X H. 3.05) Given: f(x)=w_ = 3(x+§YX *1) x —x_6 iXBix'ﬂ—i a. State the domain of f (x) . {xlx+3,23 b. Write the equation for each of the following as it relates to f (x) . If a speciﬁc type of asymptote does not exist, write the word “NONE” in the appropriate
space. Vertical Asyrnptote(s) z =' 3 Horizontal Asyrnptote(s) % = .3 Slant Asymptote(s) Q d e c. Write the coordinates of a hole, if one exists. If there is no hole in the
function] graph, write “no hole exists” in the appropriate space. Hole '2. ‘9 x =z o 3E'2')+s:] @433) ‘
2 m“: ‘= L. “'5'
x2+3x—10 _ Qt+$)(x "LE 3 x+4 ' xi“! . i a. State the intercepts for g(x) . If there is no intercept, write “NONE” in €16 appropriate space. /’ 0+5— x.?') 3 O ;
X 1"? i
x intercept(s) {5 i 0 I IQ; 9) l o 1 SXot)
yintercept(s) (O , " 57% / (7—07,? 4. (15) Given: g(x) = b. Write the equation of any slant asymptote(s). If there is no slant asymptote,
write “NONE” in the appropriate space. Slant Asymptote(s) = u 4 5. (15) Let f(x) = x+2 a. Determine f "(x). c.3—
ld X+2
v.1. ' 13+: b. State the domain and range of f (x) . p“: '2
2{‘ ‘ﬁ' ° 0. State the domain and range of f '1 (x) . D‘A: x+0
23": Eight 6. (10) Solve the following rational equation for exact value(s) of x. 7. (15) Given: f(x)=\/x—4 and g(x)=2x+3. a. Determine (f o g)(x).
we (23143) = Vans4  b. Determine (go f)(x). 3013:1173  2W +3 0. State the domain for (f o g)(x) and for (g o {)(x). (1. Determine (f+g)(x). e. State the domain for (f + g)(x). 8. (10) Solve 2” 2 0 . Express your answer in interval notation. x2—9 9. (10) Solve the radical equation Vx + 5 +1 = x for exact values of x. Be sure to check your answer.
( x+s = X "l X+s . {HamI
o u )6st '4 $2“ 0 =iXS‘XX‘IU
./ q 4—I=.l{ a,“ _' 10. (20) Solve the following equations for the exact values of x. Check your answers. a. 9426x=1 Zc7“.. [7
2c“ 9’ 63 X'* '5‘! 11. (10) Write as a single logarithm.
310gx—10gy+410gz—210gp 12. (15) E. coli is a bacteria that inhabits the intestines of animals. This type of bacteria
grows at the rate as modeled by N (t) = Noeo'oz’. N (t) is the ﬁnal amount of bacteria after t minutes, N0 is the initial amount of bacteria present, and time is
expressed in terms of minutes. Initially there are 50 bacteria present. a. Approximate the number of bacteria present aﬁer 4 hours.
Nave) = so e.°'°‘("°) b. Estimate (in terms of minutes) when there will be 5000 bacteria present.
You may want to use your calculator with the window set as [50, 500, 10]
for z and [0, 10000, 1000] for N(t).
5009' I 02 b l3. (5) Find C and a so that f (x) = Ca‘ satisﬁes the given conditions f(0) =10 and f(2)=40.
10:08 a Q=IO
7.
1+0: Ca. L
+o=lo~
r = a?“
12309 M «>0 @ EXTRA CREDIT PROBLEMS You may choose to work ONE of the two extra credit problems. The points you score on
the extra credit problem will be added to the score you received on the'last 13 questions;
the total score for the test will not exceed 150 points. ’ i
A. (5) The increasing global temperature can be modeled by the function I (t) = 0.1e0'02’ , where I (t) is the increase in global temperature in degrees Celsius and t is the
number of years since 1900. How much warmer will it be in 2015 than it was in 1940? . oz tango 12(40) . .16: B. (5) Radioactive Cesium137 was emitted in large amounts in the Chernobyl nuclear
power station accident in Russia on April 26, 1986. The amount of cesium
remaining after x years in the initial sample of 100 milligrams can be described by the function A(x) 2100600229“. a. How much Cesium137 is remainin after 50 year's??§)( )
— o z 2 5‘9
A (5'03 .2 [00 ' b. Calculate the halflife of Cesium137. @.ozz?§é 5' = wise.
Q Q..ou.9£')'t
.5 = e 5) ,6. o 21??) l'é 3 0.7.0 “5
w. ...
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This note was uploaded on 07/05/2008 for the course MATH 151 taught by Professor Hostetler during the Fall '08 term at VCU.
 Fall '08
 HOSTETLER
 Calculus

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