In the standard form of an exponential function , y = a(b)X : a . Whatisa? IY)ftlC,f,.I Y~IVf. b. What is b? b~f e 1 qeter m ,ne,.r growth /4 r, CtA c . How do you find b if you are given the rate (%)?

i. For Growth, bis: { I -t ~) ii. For Decay, b is: ( I _ V-)

d. What does x typically represent.in word problems? -trWU-

2. Wilma and Walder's Weaving Wanders bought a piece of weaving equipment for $60,000. It is expected to depreciate at an average of l 0% per year.

a) Is this a growth or decay model? g e, (i tA'j -r; b) Write an algebraic equation that models the situation: i = loD, 000 { /-.IO ) c) Fill in the table's values for the value of the equipment for the next 4 years. (Round decimals to

the nearest .hundredth) Years 0 1 2 3 4 d) What will the value of the

equipment be in l O tears? q Value of lpOOOO ~'-/000 yi1poo 43740 ~'i¼ Ce £ uip.

i = 1!>0000 ( I - .10) ID =-1'}-0 ,q20 .7 I 3. The population of termites in Mrs. Woodley's house is 200. A termite inspector te lls Mrs . Woodley that

the number of termites will quadruple every week until she pays for their removal. ,-- \ a) Is this a growth or decay model? _ ..>qg~r-=D-:..V.c___v --=-, _;__t _;_\ - - - - --

• b) Fill in the table values for the expected number of termites for the first 4 weeks. (Round to the nearest whole number)

c) \A.tri+e a ~~exl/tfow tt iodel. el) ~~C)(T -

~Ftil,g o+

Week. 0 # of

1-00 -termites

1 2 3

'300 1/}.00 \2-XOO

e) How many termites can Mrs. Woodley expec~t~a~t~th~e::_e~n~d~ o~f~9~~~=======~

2°0 (4 )9 52,42. ~~oo t -erMrte€i

4

0 1, 1.0D

4. Miles bought a new boat for $20,000 in 2000. The value of the boat depreciates 8.5% every year. What would the value of Miles' boat in 2009? (Let 2000 be year 0.)

. ':J" zo ooo ( 1- . o'BS) '1 ff 04'1 I. z.s] 5. State the translation that takes place from f(x) = 3x to each of the following.

g(x) = 3x + 8 g(x) = 3x-5 - 5 g(x) = _3x+l + 1 g(x) = 3x-4

r\gn t 5 ol ow n 5

r-ef\ect, \ef t 1 Vt,? \

6. If the function f(x) = 4x is translated up 6 and left 2, write the new function, g(x ) .

rr9 ht 4

~( -,: ) ;;;: 4 Jt :z -t-lP · If the function f( x ) = 1.sx is translated down 4 and left 5, w ri te the new functio n, h(x).

h ( iJ =--· ,. s "' 1·5

- ~

11111 -Determine if the function is growth or decay, and then identify the following :

s. g(x) = 14(0.99Y

(irowth or8 Initial : \ i..j

Factor: , q 9 'Rdte: I ~o

10. f(x) = !(SY 4

(!!!!!Ji or l>etay Initial : 1/ 4 Factor: <o 'Rate : 7 00 "70

over you, Quiz e,1, E:<pbi ,e, ils+

9. h(x) = Gf ('.jrowthore!!3J)

Factor: 3/'-/

11 . g(x) = 4(1.34Y

@or Decay

Factor : I, 7 If

1

l 2. Rowriio the expooeoiia! expcessiao iota radjcgl to~¥

Initial : I

Initial : 'f

l~. Re mite lite ,adical exp1e,,iefl ifl fe oxp.oo.en,tLalform and simp li fy if neede~t ... (JL&n/

Sirnplity o€1Gh e>tpone11liul expres~on. +21 ~ . -3x""'y•

•• J 5.- (4x ~y~ ;:;; 3 • 3yx 6

.S.~ llfy-eeeh--rodicoi"expressi('.)rr.te-ove>1rrr,eeieGl.f.orrA,-.,~

18. Complete the table for the functions and then graph it ON THE SAME PLANE.

y = 6(2)X

X -3 -2 -1 0 1 2 3

y .75 ,.s 3 (p 12. 2 L-j Y'o ~~=---:::::::::_~--+---~=d"---- ' ·10 ·8 -6 ·• ·1 0 6 6 10

·•

·s

• 10

I

-I unction that models the points in the table. J9. Write an exponential f .

( '

X

1

2

3

4

y

50

7 .5

1.125

0.16875

Factor: • I~ Initial amount: -3 3~ _ Rate (%) 05 ?o ~Jm•,• MeHI Rl:;jle:

20. Use the table about zombie ottocks to answer.

a . Fi1 ,d ti ,e expoIIeI ,tial 1egrcssion 199odel. Round to ti II ee deei11 ,al places-:-

b , Whe+-is the eoFFclation GG@ftioonW.oubis..ci.aia QM-W-hat eloe3 ii lell you~ (room:1-to-foti r cJ.e.ci~I~)

c. -1::kh ,g Our regression model. aetmmlrre-i'roW -ffle•ftlf 2omaio5 >1<iU-be preseoUn. ~..mioJ.1 l$~

Write the equation of the graph that corresponds

to each equation .

21. y = 2 Gr B 22- y == Gr Pr 23 . y = zx V 24. y = _zx \; 2s. y = 2x c

X

1

2

3

4

y

2

8

32

--128

Factor: 4 Initial amount: 1/z Rate (%): '300 ?o ~Je'," ~le1s,I ~ule :

Equation: y= 1/i. ( 4 j

-3 --- -2 ., o C ' - -~ -

' -·· _ ... -•·- ·- ---·- ;,-

I I

-2

\ \

-A~~ftto n

Wh q,f , !> q,n ~s~111ptote, , f\ how cl~ ~ov th& .,~rtnt -fvntt(on f(x) = b" 'l,n .,, ,n

r Lx -h ? fvnctron g(x):::.a..,-o -t-k •

,t rn both ;-rtA n sfo r m e.cl

hon z-on~ I lrn-e ~ovr- fvnct,-on qt1tS close to hut nevi r c ro~~.e. s. 7 (t?arenr Fvnc-1loh") q~ymp-n:rrc, ,-5 ~,w~!1 s 'I== o -)(tf""insFPrml-4) rt\?rt.st-nt s asym;t7Jt-e

5o\ve. CD 2 5 )(-z == J..

----.. 5 ~ 1-()(-.2) = \-'

2'i- - Y = -I 21- -= 3 I A -= 3 /;;_ )

@ ·2 )(- 1 .-4- '= I '5Z )( -I . 2_ 1.(- 1) = Ao

~ e

i -1 + (-2 ) -= 0

1--. - 3 =- 0 [x = 3 /

- 1- + ~-;:.\

@ l-\~z,( - 1 = 3~ 3 r '

1 ,2 (2.1- -1) "'?, t1x -z::; 3

''1 y, ;- 6 ~2 ~/ 4 ]

- 'I- :,: - t-[X: :i]

,(:\ I (z)(.- 4) ~- \ l2 ;;;. IY~ r--1 ('2-'1--'-1) p-2

-Z.X-t'-t -= - 2.. -2 -y,. ::: -ft,

~ = 3)