Name. _TriglMath Anal III Date. No. _Quarter 4 LoP rractI" QUh

Simplify. write in exponential form

1A. (x4l)~64xI2y-6 lB. ~64xI4y-3 ldt 'A X. 14/4 ~ 4~

r,";-'lfrf»L! ~ /'\1-"1>-~-'/1 2B. ~8X6l .18xl2l

(J3"J'fX312 ~N. (';13)J3x..'f 8t3

';).Z/'t ;(12yN. ;)' X"4 3/3~ I :iN;'\ -1Y~h

2A. ~16xsl +V8x4 /

3B. 3s,/3 . 81'1i7 + 9.m3A. 43.)2 ·16./8 +8.)32

56 1m~.( 34)3~ :) ,3 =( 83'1.1

(32 )2f3 34~

Solve.

4A. Zlog, x -log3 (x + 4) =log, 2 4B. logs x -logs (3x -4) =2

~0Cjs -L == d- ISX-\ro=- x. .3X-LJ IX= lro5'2-= ~4- 1~

5A. log, x +log6 (x -5) =2 5B. log, x + log, (x - 5) =log614

J.0810 xCX-,::» =.QDj 101 4 X'l-5X-14c.O

)('- 5)( ~ 1"1 (fiX~'Vl. ") '/.. ,'bv ~

6B. 22.1' -6·2.1' =166A. 42 =~( 5- 2x t

JX ::LX ~ -lo ' . -10==0 J.~~ ~

(~X-5)(~x+~)~O [ X=3l

7A. 32 =14e(2x-I) - 3 7B. 83x-2 =ifl6 qX-lo= 4­3(~~?-= 1'413 [X= ;LJb~!:;I~X~ ~ :fiiJ

42.1'8A. =48 8B. x =logs 8

LY-.= /.~d-]~=~~

--- - - - -

9A. 9:1 ·'·-~ =~

118. 53~ =27

Continuous Interest: Compound Interest: Growth/Appreciation: Decay/Depreciation: Exponential Exponential

A = Pert A = P(l +-;r' A=P(l+rY A=P(l-r)'

128. A calculator cost $48 in 1974 and $20 in 1982. at 4t 'Yo compounded monthly to amount to $48oo? 12A. How longwill it take a principal of $3500 invested

Find the cost in 2006. e

XJ== 45 (I-r') .4r1~( \-r )8 ') '/g

•~C\lLJ::: l-r .la-t= r

13A. A city had a population of 28,200 in 1964. 138. Money doubles in 8.2 years compounded Assuming an exponential rate of growth of 4 .5'Yo, in continuously. Find the rate. what year will it reach 50,OOO? c:Jf< ::- 'R e,~ .'IX

eB11X. ~::: I

\b\ ~= ~,?r ~ [h45tJ r ~ ,OfSli5

14A. 35 grams of radioactive material decays to 20 148. 17 grams of radioactive material decays to 3 grams grams in 420 years. Find the half-life. in 125 years. Find the half-life.

15A. $6,400 is invested at 2.4% compounded continuously. How much will the account be worth in 5 years?

16A. A gallon of milk cost $0.35 in 1942 and $1.29 in 1984. Assuming exponential growth, find the cost in 2006.

17A. $4,800 is invested at 8.25% compounded continuously. How long before the money doubles?

18A. A $1400 computer bought in 1996 depreciates to $650 in 1999. What will it be worth in 2oo1?

19A. A teacher's salary was,$42 a month in 1907. Assuming an exponential growth rate of 4% find the teacher's salary per month in 2007.

15B. How long will it take a principal of $1500 invested at 2t% compoundedquarterly to amount to $3400?

16B. $1,400 is invested at 3.2% compounded continuously. How much will the account be worth in 8 years? •

A = t400e:O~8)

hl~.4~

17B. A city had a population of 24,500 in 1982 and 48,000 in 1996. Assuming an exponential model, estimate the population in 2008.

4ela.D == 94:x:c(1 +r)l y.

l.<1LltI1((l+r-'y~f)VILf ( '\ [2 _ A a rvv ""'\ l-t,04 C1 )

\,oqq = l+r A~

r=, D4q A=\'BS22l.0cl] 18B. A calculator cost $84 in 1970. Assuming a depreciation rate of 2t%, what should the calculator be worth in 2012?

A = 54(l-.0'15)42

A=I~~J

19B. How long will it take a principal of $2,300 invested at 5t% compounded quarterly to amount to $3,5OO?

?X::J:)::):: .1:ro( l+ ,~S ) 4t

\.52= (\.Ol~15)4t J Qj 1.01 ~ 4t .Q,(X\ l.Ol315't; l.lo1 \A fS\

Name. _Trig/Math Anal I dl-M QU~ Date. No. _Quarter 4 ...,.. I'JI".....­

Simplify, write in exponential form

lA. (x4/)V64xI2y--6

x+ 3 uA Y3Ay.~-'2

~ 2A.Vl6xsl +~8X4l

10/3XS/~~:3= 'd.4!'X -VIa_~ f/lbX7i3if12 t L ~- - J X

3A. 4J.J2 . 16,)8 + 8m

aB (;/~yr2. . (~~ 'f~ = ~VJ FJ..

lB. ~64xI4y-J

2B. ~8X6/ 'V8x12l

3B. 3sJ3 ·81m +9J12 .

= (J3 1fl \~~ - ~

Solve.

4A. 210g t-IogJ (x+4) = log) 2 QJOC\3 IX z: _Q tXj~ X =l X+3

~ X+4 )(2 'xZ_ ~ X -ii~ X+4 =-1 (X- 4 1(X+-c;')\4 w--:f/J.

5A.log6x+log6(x-5)=2

t '2-5X- 'JltJ ::- 0JOj\J> X(X-C:J) =- 'L (~-q ' 1 (~ ~)::; 0x..'2.-sx -= lL)J­~O'( -)(

6A. 42 = 14(5_2X)9

l'i ~ r:L4~~ ((S -LX)\ )~ 3?:F~~ Cj-2X t '1--= - \Ltf) \

7A. 32 = 14e(2x-')-3 I 1 ~n 2..S:(2)(-l') ,~= 14e-Lx­

1/5::- e- 1X-1 0=.Qs5\ ~

8A. 42.< = 48

~x QDg.q =- ~o3 48 (}<=\.:'AltJ Ix-:: .lCf J-. ,

4B. logs x -logs (3x -4) = 2

5B. log, x+ log, (x- 5) = log614

6B. 22x -6·2X = 16

7B. 83.<-2 =~

8B. x = logs 8

~X-~~ 4-/3

Lox= 1Lq' ~

IX= 8{Cj lOA. x =log814

9B. 42 = 12e(3x-2)

lOB. 18::: VC2 -xt

11B. S3x::: 27 ,

Exponential Exponential Growth/Appreciation: Decay/Depreciation:

A:::P(l+r)' A:::P(I-r)'

Continuous Interest: A::: Pert

Compound Interest:

A ::: p{1+~-r'

12A. How long will it take a principal of $3500 invested at 4t'Yo compounded monthly to amount to $4800?

45CD:::. 3~ (\ t- I~~ i 2 -t

\' Jl \ ~ ( \,CYYJl 5)\1:t

-.Qog l.'Jll ~ [?t .Q.t)j LmOl'S I G::. 11111::' \

13A. A city had a population of 28,200 in 1964. Assuming an exponential rate of growth of 4.5'Yo, in what year will it reach 50,OOO?

SCX::OO== '2-1S1CD(It-.045;t \~ll~:; ll045t

Jog Lll~:=.t .loS L045' -t:: l~ LCl ld+ +lJ:: I~lCj-l---'l\

14A. 35 grams of radioactive material decays to 20 grams in 420 years. Find the half-life.

:1)::: 05(\_(')4'2.0 Y~II Lt'1.D\ l/ f W ,t

1- 5l -\.(l-rj ' ) lO~x) (l-,OJIJ) ,ClC131 ~ l-Y .S = ,oel'Bl"t ,())I~= r -- Qnq ~ 'S - t ~ .Cf '1 n

12B. A calculator cost $48 in 1974 and $20 in 1982. Find the cost in 2006.

13B. Money doubles in 8.2 years compounded continuously. Find the rate.

-14 B. 17 grams of radioactive material decays to 3 grams in 125 years. Find the half-life.

15A. $6,400 is invested at 2.470 compounded continuously. How much will the account be worth in 5

years? 02Lies)A -:: Lo4lX)e'

Iitld-\5,C1(3 J

16A. A gallon of milk cost $0.35 in 1942 and $1.29 in 1984. Assuming exponential growth, find the cost in

2006. . A2.. I. ~Oj:: ,3':) (I +r") 3. tA\~1. (( \-t r)42") IJ~1.- 1-1­

A == \.lQ(\1- ,DJ'Ll \,O~1-::; l-t 1

t> .O~2 r $> (L.~J 17A. $4,800 is invested at 8.25% compounded continuously. How long before the money doubles?

18A. A $1400 computer bought in 1996 depreciates to $650 in 1999. What will it be worth in 2001?

lP~= 14CO(1-r y:.> /11 /1 'l:z ({ _ )3) 'f3

"JVrT - ~ \ r f.\.== ~~ (.lll.{ )~ .ll4:::\-r

. 'dd\tJ ~ r (it 3'5Q.40 J 19A. A teacher's salary was $42 a month in 1907. Assuming an exponential growth rate of 470 find the teacher's salary per month in 2007.

A - 4d(I+.04)lDO

[It .9.-1;}1 ,;}Ij

15B. How long will it take a principal of $1500 invested at 2t70 compounded quarterly to amount to $3400?

16B. $1,400 is invested at 3.270 compounded continuously. How much will the account be worth in 8 years? ,

17B. A city had a population of 24,500 in 1982 and 48,000 in 1996. Assuming an exponential model, estimate the population in 2008.

18B. A calculator cost $84 in 1970. Assuminga depreciation rate of 2i7o, what should the calculator be worth in 2012?

19B. How long will it take a principal of $2,300 invested at 5i 'Yo compounded quarterly to amount to $3,500?