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Unformatted text preview: Fall 2007 Math 151 Test 2B {i
Name {% 0...! 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. 1. (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. Pledge (Sign your name) (1)5) Let an be the leading coefﬁcient. Write the complete factored form of a polynomial with real coefﬁcients that satisﬁes the following conditions:
Degree = 4, an = —3 and zeros are —2, imd. 3 3 (xiLYxCXMUCnﬂ 2. (5) Find the complete factored form of the polynomial, given that x = —3
are zeros. f(x)=x4+2x3+x2+8x—12 64'3Xx") = Xz+3x")¢ .3 3 qurZXS '8—
‘  2
x +Z" 3 x9+ZX3+x +?¥"z ' x4 +Zx33x"
«kWhI?—
sziﬁx n.. 2 ~z)
3(15) Given: f(x)= 9‘ '4 . g 6*“)!
x2_x—6 a. State the domain of f (x) . ix lx¢3,2.} 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 Asymptote(s) X '5 g Horizontal Asymptote(s) QE 5' l Slant Asymptote(s) Mg“ E 0. Write the coordinates of a hole, if one exists. If there is no hole in the function/ gr ph, write “no hole exists” in the a ro riate space.
I— “ z ' “r 3'— Q zr‘s 4. (15) Given: g(x):w_ (X + 5K)!" 2) x + 4 x 1 4
a. State the intercepts for g(x) . If there is no intercept, write “NONE” in the appropriate space. /'~ (x+ 1 ) o
x intercept(s) x+ 4’ ‘
y intercept(s) 0 " 3/2. (0+ ‘5' )(o  Z)  T3... Fl"! b. Write the equationof any slant asymptote(s). If there is no slant asymptote, write “NONE” in the appropriate sace.
Slant Asymptote(s)
_ x’wh:
'Xl0
X ‘+
“(c
5.(15) Let f(x)=x:5+2
a. Determine f‘1(x). (%+5)(x—Q_) E: ‘
= —l—— +7— %+5 3 —'—
)uS' x—z
_L_ , _l__ 5
X= (3+5 +1 ‘6 xJ.
.. = —£— " ._ _I_ 3
x (3+5 60' xz b. State the domain and range of f (x) . D5: MES'
22F % t 2 0. State the domain and range of f “ (x) .
33" 3 1+ 1
2x4 : 3 "F": 6. (10) Solve the following rational equation for exact value(s) of x.
3 v 7 x+2_ 36—3 3 (x3\ = 7 (x +2.3 3x9 = OxrH'
“'23: 4' 7. (15) Given: f(x)=\/x—l and g(x)=3x+2. a. Determine (f o g)(x).
ﬁgs (‘3: % (3Xf'2—3 a q “I b. Determine (go f)(x). a
ﬂag 0‘)" % (‘xI) 2—x
x29 23: N? o xzz’gla 8. (10) Solve 2 0 . Express your answer in interval notation. 9. (10) Solve the radical equation x/x + 5 +1 = x for exact values of x. Be sure to check
your answer. _ “#5 = Xl
x+$ : x12x+l
X= an=—l ' 9;; V?+:.+/
(7TH +I® 10. (20) Solve the following equations for the exact values of x. Check your answers.
a. 11— 36" = 2
 3 e”: — ‘l
e’" = 3 m=1wv3 .3:‘ = 2X'3
u Lat3
3 a.
I "X d. log5(x+ +10g5(x—1)=10g515 Loci (xzU zﬂogglf S 11. (10) Write as a single logarithm.
210gx—10g2y+4logz—logp 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, N 0 is the initial amount of bacteria present, and time is expressed in terms of minutes. Initially there are 62 bacteria present.
— a. Approximate the number of bacteria present after 2 hours. N020) = (926020”;
: GYLD" bum b. Estimate (in terms of minutes) when there will be 3000 bacteria present.
You may want to use your calculator with the window set as [50, 500, 10]
fort and [0, 10000, 1000] for N(t) . 3000 = (028. ' ~
{73.74 mum . ~ i:
———
l3. (5) Find C and a so that f(x) 2 Ca" satisﬁes the given conditions f(0) =10 and
f(2) = 40 . [0: C00 '7 (Le/0
‘fo =' CollV a} , if
ﬂog/0Q a. = 1” 7. bui 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. A. (5) The increasing global temperature can be modeled by the function I (t) = 0.1600”,
where 1(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 2020 than it was in 1950? '07 “0)
34‘1990 I (#03 ‘‘ JeC I
9:, .22°¢ in. 10:5 1301;) _._ " énvylis) a: I.o°°C« B. (5) Radioactive Cesium—137 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) = 1006—00229“. a. How much Cesium—137 is remainin after 100 ars? ’0
g 2% 'oltqs’ ...
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 Fall '08
 HOSTETLER
 Calculus, Following, Christopher Nolan, Slant Asymptote

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