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Unformatted text preview: Math 105 Mid—Term # 2
Show all your work to receive full credit & box your answers! NAME \KEE: (please print) Score / n E: ‘5”
True/False/Fill in the Blank
l .)1 5pts
a.) If f ((g(x)) = x then f (x) & g(x) are inverses of one another 'T ®
4 ‘ .
b.) If y = 9182%? then x =  4 is called a iiaiﬁi Cir“ rQQmmEE 33]”:
x + on the graph of the function. co (fog)(x)=f(g(x)) ' (:13 d. ) Ifdiﬁ'erent numbers in the domain of a function have diﬁ'erent
outputs, the function IS called a l, "e \ function. e.) y = b" represents an exponential function if “j? . '3: \C‘; 3‘35: X, E; jigR f.) The y interce ntfor all exponential functions of the form y= ab" where a is a negative 33: —(L 53. 3w —L—2>4’“= g.) In order for an exponential function y = b" to be a decreasing function What must be
true about b? Q; \QJNE h.) The continuous compounding interest formula is P = Ige” (if) ' F i.) log]: €32 log10"= E, log10= E j.) e'“ = 23 lnM" = X ig} ﬁg M is a positive number
k.) If M N are both positive numbers then log(%)= Lag is; ’4 \ﬂ% M '
en 1.) Change the base from base b to base e of log, 7: = §ﬂ "3g ‘ I
\n b Math 105 MidTerm # 2
Show all your work to receive full credit & box your answers! ‘ 2.)10pts Tell me how (using shifts and translations and stretching)
J: f (x) = % (x + 2)2 —— 3 diﬁ'ers from the basic graph of f (x) = x2
‘ (Sketch both to help with your explanation) £92. ‘ I
b. Kama Jan (A (M f"
.2\ gbngﬁa—m L299? 2 do 1T5; '
33. Mars: ALCqu 3 nema 4‘5 ”SAFE Wm: ﬁnalC.) a , , _
miﬁ 3.)10pts. Sketch a graph of y =—.x—il— be surevo label: asympto mterceptsXﬁ O
5 ' x2 + 3x+ 2 ’
puncture points. \
ll? &+'%L+33 _ “1‘
New” \J {3‘ 2 1: ~:2
egﬁ‘a’ Ma Q; a: \.
i\ \DTESCEQT = ‘/ 2.
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4.)10pts. For f(x) =—:—, Asx ——> oo— thenf(x) —> F) ? and
as x90, thenf(x)—> 4 v0 ?
was" ”“—
5Wﬂ’ 5.)10pts. Find the inverse algebraically for y = —1— — 5 and prove it is the inverse by I x
. showing that(f °f;1)(x) = UM1 °f)(x) “"’ 9 a a .
‘ﬁ " _\ ) Sifiﬁ » \‘.I “T,”::_:1iai; \ , ’—
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'POQ/Jl: 4 Li’z)‘: IESTSZ—b ><\ Math 105 MidTerm # 2
Show all your work to receive full credit & box your answers! 6.)10pts. An initial deposit of $15,000 earns 8% interest, compounded monthly at
Little Kitty bank. At Mr. Chuck's Bank he pays 8% but compounds
continuously. Ifyou plan on keeping your money in the bank for 5 years,
how much more or less will you earn at Mr. Chuck's bank rather than Little Kitty Bank? $1155
% A \Smc) C\+‘@\3§ =— Q 215% Ag
\95 $12“? . \SDDD 5%» = as 3540» A a AQQQJCDCCi CBQ WM“ 7.)10pts. Find the value of x for:
log25x=.5 x= S log3x=—4 x= \
<13 \ $5 $05133
8:Z/ Using the properties of logarithms write the following expression as the \ logarithm of one quantity W
S"ii/9w?)10g(xy+y2)log(xz+yz)+logz = _'________________
q 6L4:~\L2\ _—_ log M62 __. {Ohm
x2 «Lsz 2L><+a\ MA.
LQL 31.14% »
q been F My“ 3
9.)10pts. Using the properties of logarithms write the following expression in terms
of logarithms of x,y,&z
3 y _ “ \/
logJ; = [ASL—«(3835 ——\DL~;&£Z\3
J72 . ;
ibav —— \cﬂl’ﬁt 25: V3 \orsxc 4m. A Jr V3 \ah 2— '_ :7 :‘2 1&3th ——\c)c—1n + was] ,
XIX2433 =0 10)10pts Solve 5‘2 =2” PM
2 S _. r
2 mg)“ \MJ‘ — XZmbréme..
%: £1“le : XZ': ‘;ng :7 X2: Qa‘x':5<
r\ Q7; . Z A >~
301“ 1ng =03gx) PW
\QVV"V’V“\‘VVV"'VV\‘ 'U X: t or“ X: was)
LL13 UK“ A f»;‘ E23 \C .E “(NE 731C, \CDGIX O or“ \DgKi Q Math 105 MidTerm # 2
Show all your work to receive full credit & box your answers! Carbon 14 dating formula A = A02% where the half life is 5700 years. 1 1.)10pts. Only 25% of the carbon 14 in a wooden bowl remains. How old is the bowl ?
Age of the bowl :— “ﬂL/Sioc \43 a = LL; ”Ar/5400 '2 Sign. 11%,: ~Jr Jr: AHQQ
, m Av 12.)10pts. f(x)= x2 if0<x32 Graph the following being sure to label everything of importance. 1
l [3ng x <_ ‘3 4—2xifx>2 13 )lOpts Population grows according to the following: P = Poe'“ , WhCl‘e P is the
population aﬂer time t and P0 is the initial population, k is found
experimentally and is a ﬁxed number for each type of population.
Suppose you start with 100 kitties and aﬁer 9 months you have 230 kitties;
How long will it take for the population to triple to 300 kitties? \L Q
Qﬁ’inxmsaﬂL3 ELLA&,£;X M.
23b ‘: a“  his 2 3% L2,: = Curl. \ 0L) 0 ea 95 (+3
Laigkx Amos , 3=a —, L?) :3 a BCLQSLJ;\ 5% :At‘ 21);” \\\agﬂt_ sOQZS' _ muﬂn ...
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 Spring '08
 Hale,Charles
 Math

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