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Unformatted text preview: 1. (8)
2. (12)
3. (9) Consider the curves in the following ﬁgure. Match curves I, II, III and IV with the
following formulas, where a is some constant strictly greater than 1. a. y=—ax§_]—_[I I II A population of 15 .8. million people grows at a constant percentage rate. Determine the size
of the population 20 years later if there is: kt
a. A continuous growth rate of 2.9%. '> DL+B= F0 8 686109qu ___ £8.22 1%?”ka ' t
b. An annual growth rate of 2.9%. ‘7' PG‘) = Po lo 15.6 (macaw: Rank the following three bank deposit options from best to worst. Show all work. . . 36:5 '
a. Bank A: 3.04% compounded daily Po U + 035 a: Loaocl b. Bank B: 3.1% compounded quarterly R; (1+ 333“ 7t l03 l "l 0. Bank C: 3.06% compounded continuously pa 9080309 a: W Loan 4. (14) ' Solve the following equations for x. Solutions Should be exact.
a. 5x =17 V M05)" = MM)
)L 4:45) =1 MO?) «QUV’CQ‘Q \\
M {2%) = (ﬁx +7» ' M5140) i\
In (1W) ~ _,._. ' 01x6
MGMQ 5. (l4) Solve the following equations for x. Solutions should be exact. a. 51n(2x—3)=l7 H/S
i? a +3 = ’5‘ X:
\4/5 W 9‘
Qx—3= a J
7}
9~>L= 6‘ l5 *3 6. (12) In the following problems, convert to the form Q = ab’ an_d identify the annual percent rate
K
of growth or riecay. b 5 e/
a. Q = 6e0‘7' Q ; (Q (Q‘DMYC
K  QD‘? A, ..
8 ' a "" ‘QDM "b [01.Lf°[oamm+k
't
Q:QCQ.D[%> 2) 10: Hr a r = \o l
' = 2.01% ~1
T— . ‘5. {OX .4
b. Q = 789‘3'4’ ‘ O “’i 7°
9:34 it .05?) =b
Q = :Irg @0333" ——> F=.o%% \
" " «We? 3 "(762370
7. (12) A family of rabbits begins with 6 rabbits. After 5 months, the family has grown to a size
. of 176 rabbits. Assuming the growth is exponential:
a. Give a formula for the number of rabbits as a function of time in the form R = ab’ . V
0t=C<> =92 l%=(¢2b"5, ‘32 Pia—:55 :e 302%ng
' t
bx 1.3(2‘3‘ Q‘éUCICQSB
‘L
L} ﬁle; = (o (HMS)
b. Give a formula for the number of rabbits as a function of time in the form R = 06“.
b =el< 1% K = MUD} => K=lrt (HMS) % 0,0,}5
0197's 1:
R = (o e ~
0. How long Will it take for the family of rabbits to be 50 times its original size.
(AM. anocan— [a °Fb)—~
r _ . (97151,
usmé Q'CQ 9’ ‘ L \ SPEC; moldl4)
 (9751‘: v\ 50
eoo=Coe tr w 253%
. . (OKt . 5'
SD = 9/ MED) = torst 8. (16) Consider the function f (x) = J; — 3 . For each of the following, determine the formula of the new function and describe the transformation that has occurred to the graph of f (x) . New_ formula Descrition of Transformation y=f(x+2) st Lift annals
y=f(x)—5 swat W 5 0MB
y=_f(3x) Hort Compt‘QsSlEM by '/3 x— onaS meQdLém
\jCAKLS (VPch ‘
VarH _ (moMSSLiN by ‘19. 9. (10) Determine the formula of the following parabola. {Ix} = OLLXhl 'L +\<
ammo—331 +6 5— éuCo—gf +8)
5: *8) 3:ch é &.=”\/3 10. (10) Consider the ﬁgure of y = f (x) for the following: 8 .
ﬁx)
, 4’
Next consider the following transformation of f.
3!
12 (geriw
i “x
A; m m m mummy: m. m y = S
6 a “we 4 8 1216 2b a. Describe (in words) what transformations have occurred. ~> x—ooors (nﬂaclrm
—> MAW straight by Q ‘CCLCiOV‘b *1
>2 StuH, 09 8 b. Find a possible formula for the transformation off shown. Given tiﬁ .  , {IQ ——> )UOUQ'S (EV. {3Cﬁg3 —> horii. 6M
391x) +8) a cart. 51ch “Have 11. (10) For f (x) = x2 — 8x + 9 , convert the quadratic into vertex form by completing the square.
Then identify the vertex and the axis of symmetry. anauagar4%r%Mua ADM =w 4o +q
rm: (wait—:6 12. (12) 13. (11) Using the given triangle, ﬁnd the following: Solutions should be exact. . 01
a. s1noc= f’ H 2W0 b. sinﬁ= T
_ 2E5
c. cosa— #—
H d. cosﬁe fa— A spider spins a single thread from the ground to the top of a nearby gravestone. If the length of the thread is 3 meters and the angle between the ground and the web is 32" , ﬁnd
the height of the gravestone. Mo WW5 32° 7 51n(%1°3='*‘g” /
7 = 3~ men") x New Extra Credit (10 points) If you need $23,000 eight years from now, What is the minimum amount of money you
need to deposit into a bank account that pays 4.5% annual interest, compounded: At =Pl 3t
‘1 a (+r a. Annually? 8
93°00 : P OMS) $ No 11% 2e
_ 2300b A' ' ’
P' Lions)” " M7 W34“?
aast
M AL+§=P (warnsl
b. Daily? ups Cg>
ascoo=POVZjé , Macaw!
23000
@é We» :2 HoweCf!
0* aces c. If the interest in the account is compounded continuously and you only have $15,000 to invest,
how long will it take for your investment to grow to $23,000? 230cc) = 15000 em“ , GHQ? SW5 (5000 MCza/ja m
[‘4 = .Ol—i‘St =~> t; log—S A” ...
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This note was uploaded on 12/23/2009 for the course MTH 151 taught by Professor Mason during the Fall '09 term at VCU.
 Fall '09
 Mason
 Calculus

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