prcithce, iVIath 1090,OO3 uizO 2016 SP

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prcithce,
iVIath 1090,OO3 uizO
SP 2016
iiID #:
Class ID #:
Instructiolls:
• Please clear your desks and remove headphones and hats during the quiz.
• Show all work, as partial credit will be given where appropriate. If no work is shown, there
may be no credit given.
• All final answers should be written in the space provided on the quiz and in simplified
form. When needed, give your answer as an exact amount, i.e. a fraction or symbolic
expression, except for dollar amounts which should be rounded to the nearest cent.
• Scientific calculators are allowed on this quiz.
AXES!
LABEL ALL LINES AND
• If your phone is out during the quiz it will be considered a cheating offense
put your phone away!
1
-
Math 1090.002
62s
13 November 2015
1. Carbon-14 has a half-life of 5730 years. The amount y(t) of carbon-14 present after t years is
given by y = yo() O where Yo is the initial amount present at t
18, 000 years, if the initial amount was 10 grams?
0
f1
=
0. How much is left after
10
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13 November 2015
Math 1090.002
2. For the function f(x)
=
2 log
(x)
5
—
1, answer the following:
(5
(a) What is the domain of the functioi?
(b) What is the x-intercept?
(c) Sketch the graph of .1(x):
(cc)
VI1) x>O.
por 29c()c_ 1 VXIR
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1I1a(v?:
(b sef f(x)o
()- I
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(b)
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7. Solve these equations. (Note: Be sure to check your answers and state only the valid solutions.)
(a)(1O points) 2
(x
3
log
+
4 x—2)—log
x=1
3
(: L4(C +V{ t(L4
Ic
Cx
1?
(Qv’L
X-41X--2..
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+j’vZ, to
t4(i(-2\
2
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t4x_X
f4x-L_
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x
x
X
hOt (
(b) (7 points)
I’
3
Kl (xlXL)
2
0— X
I
Solution(s):
.
)
2
log(x)—llog(x
uv
pr’ope’f-tkL io
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(ft1t
Cowb1v’
cpreccoV
/t
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1
1Ox
—
)
X
Solution(s):
(c) (8 points)
c*;
2000= 70
05 2000
•
1
(
)t_
tV
2
(Give answer rounded to nearest whole number.)
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=;
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}
c
Solution(s):
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Mathematics of Finance
Part 1: “Leave it Alone” Finances: Compound and Simple Interest
t frLLS h- C ç1wL
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pdd
c__ur Sr-\
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(V7f+1cP(Jj
=iLeci o
Three Scenarios:
(1) Simple Interest:
A
(a) SC€cU
a
(b) fri
wvq,
es-f
c-t W’Q
i
(d) Variables:
•
S= th-L
•
P
•
t
r
PM 0
-ti
-the a n i+ia ( I
pn ncp L ci. rL.
a flV)L(CL
-
VV4-&Q t*4
XO(4-1Al
(e) rpes of Questions:
(LVS i’4” /L4fli
1
(h1e4’e+ Vaft
U.rj
jv.-ufit-f
,‘
S = P + t (Pr ) P (1 + rt)
(c) Equation:
•
is nv s-1e4 d h-L
ctvr 61 ec{
S14 r
sl1rv
is
a
‘
dS
Hc U
1/LC h
(2) Compound Interest:
tLrc’oI 2
sc,ivi’ i rivr4
(Y)VSl
&
irs i we SkCI d-t * ‘L
.etrred e&-ecw-t fre t CLO I4A
bf) SU frY
(a) ECE41 -fl
is.
a tvi V L’w
n-/ec€S1
(b)
)
S=P(l+
—
1
(c) Equation:
‘5: Y’,
(d) Variables:
•
S
•
P=ifQ
•
t
=
•
r
=
•
n
i1 dCco L,LV’f
=
VcL4A-G
,‘rintpL
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LAIrZf
4
=
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ct
./e4rS
t4e4 ‘es-i
d &(
co
t1”-’2 IUYlAf2 SU fri
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rcrl-e
rd
(e) Types of Questions:
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VY)
A
CA-
n— L I —QLf
Cti
lfrk
o
1AIC
fV\d
I fl I LkJ)
(3) Continuously Compound Interest:
CnO-rfo.’
(a)
-1-j irQ
(1
v
4 1
iS
n yecd
cd•
fl-i tt’i(
4IV
COriy2 CYA’V’Oj 4 O7VtI’l ‘?
j.-vrjt’e/ is -f’w,
i
cptI
“/,rv’-d
(c) W9re’e’com
‘1J41
(d)Equation:S=Pe
•7- Drry)
C--
(e) Variables:
• S=
;i42j.t9,
•
P=—Lkt€
•
=
r = —/A
•
w’J,e+—
C I’ThU
4,
vau a-f
â(L+
-
OflW
4
1i0iS1
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e.
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cU? ci’iJid 1 itk
(f) Types of Questions:
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iAPY: What if we want to compare the totalinterest earned across multiple investment methods?
(1) Simple Interest:
APYzr
(2) Periodic Compounding Interest:
APY(1 +--) —1
(3) Continuously Compounding Interest:
APY = er_i
APY is the percent increase in your account over 1 year.
i.e. the simple interest rate necessary to earn the amount of interest
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