I. :.J.:

Name

3. (_~)-4_ (_ '?")tt_ \i1\3 - ~-ru

5 .• -,_ Lf,,-_m4-2 - L-/- '! -BJ

\0'!> _; S.;l 55 ~ ?''5-;.~125-3 ·25 = . 0. eo

7. 5-6 '=>--~,

Simplify, \~-'5oj(5a) -, ~

9. b3 - \0

11. 6a·2 +9a2

sa

~

q d-_~-t- ~ /

~").a + ~a'f I

4... ~.3-3, _~.i..~--s ~1

&\.y C\ ED-273.81-1 - 3 • ~ - - ~ - ~

6. 92 a4 - ~~.. :;._}

~ '-\ 5 ~8. 16·32 ~ ~. ~ . 2. z: ~

4-3.;)""2..

~ 3a2' _12. a/' 2~ ~

lXJ;

L\

~ 'T ----.-_

13~'c~/{ _g~(2xy2)2 - ~,,(i" Lt-yl-

15. 8a2e3

c - ~.36a·3~c2 -~

17. 3x2('3xy,,13).'L{ 3-.'1 'g". ~)-1.<")" ~"2 " ,"'_i.)" -I - .,,-

19 8n" - 4n-2. 2n-c' '. . 20 (ax'r'!\:¥(\ 'i '!,Ill 'E9J. ~ .a-'x-2- = 9-(\ -;z~r1-~ 1- --:-~21. an+1·3n+l

an·3n

¥t'+I-A" ,«H-"A-n. . 3CL 3,

~ J • ~

",

Date Period__

WORKSHEET - LAWS OF EXPONENTS

EvaluateWithO[ij,a calculator. 51. -(-1)";:: _ \ 2. _22':23 = _ .;;.

=f3:2, \

il

14. kV •• - e :;(e ~/(' J - X 'f.. :: ft_J

16. (4r252)2 ~. '(J S« [D

(4r25)2 - 5{QJf" ~ -

18. ~ = s-i-3'I~~j2. ~

aX' ~0- y.;l : ~

22. (a-2,+6-1t2 _

(~ f ~ )~r 24<3)'-;;2..'( ..,\ ~~~(~)_~ . '

Q~)?-~®~.5 ", ~5 ,

f_ I _ ~ _ ....,__'-.V,.., -:. ",.,." ,...l 3 ~

I A 7-2 IName Date Period '[',":n_2

.'"\0... -;;"a_WORKSHEET - RATIONAL EXPONENTS

Evaluat~.=oo

(9)2 2-1. 25 -.5

~ z,-l1\2. (~)l: ( ~)~:- (%)W 12 -'12)x·'12(2x' - x

17. x., _I/~'h("1'J.'h_X )

'i-g X}

(g_ [J19. (E'f -2- I

(fi;)~(J.'/) ~73.125~ -=@ ,,,-; :0 ~v~:O I}j

If 2_~6. .J44 :: i-z: z: '-f ~2 l...~1 3 _ 1 -

5. (- 64) :: ( 4) - 110

Writeeached~ simplifiedform,usingpositiverationale~r~7. W ~~ 8. (s;7 z: (Cb'i!) ~~

3'~ .J..~ 'l -t., '2. ,~9. (V1SX-Y:: (~to)C) := 8 -x.) 10. V27X-"y2 ::- (~1",

-a'V~r/:-=3Xj ~ <:>~. • 'j..

12. (16~~. \ 4>;-~ z: (it- ) o/~

-)ij14. (16'12 + 4'12)2

(~+~);>.~(o~::r~l

SOlve·s!

21~

~

~l- .i23. (x+5)3 ~(16)'J-

~I ..1- 1 11. fX'~+'¥X~+ --, ..1.. J_ "'"Lt ~ ~ y..'tX3 I1_l-::1t 'A9~ -:::- XPi (p 13. (3.2 + 4'2)"-'12ts, I ,Y1.,,'1 "'tt) ,

l&)-~(I'+t.j)~\_1'14- ' ~5

co\[l

I A 7-2 I

18.... -w 't"-;;}- r;:l(.'W'" 7jfn ~l±E::.J

_ I I _/1.q;;~ I1 _;:... - - .....' ~ ~,~l>

20. ;:; '_.1riar~; ,,1- ,IP

- ~3x.'0~1.1

2

24. 4(X_3)3 =16"it ~0~LX-3Y::: Lf z,

X-3-=- 'Bto=J

Q + g_ . ak> ta.. '"'-J..-1 b ~ _~ L 2-

19. a +ab -=" .. _ b 20. b ::: D,ab-1+a-1 a... ~ o,'Z..'~'''b 8bX ·b-Y. ~ IdV,'2...

10 ..0...___ \\J O-...P , .... '0/ _ ,.'"

- ~'o","o.....• ().~ . " ~ ,:J ~ 8 (.-7;/'-

, - Y,i 6.2t'b j .:.1~~.I '1/o.-(a..'o-\o...) l I '.' -=-...._ 12-~ o.?-l'b . 1 . 'I ,~- ~

I '

t 1 ]-221. 25-2 + 2-2

t I ._2-

-t-,-/)"5..1±2

;:(.0 )-

(G) \- ...-~ /2l)~)~:::,'~

~I

I A 7-31Namei _ Date. __ Period __

WORKSHEET - EXPONENTIAL FUNCTIONSGraph each exponential function. Write the asymptote in the blank.1. f(x) = 2(3') ~ II -= 0 2. f(x) = 2,,·5+ 2

Exponent Practice. Simplify.2a3b _ ~Ol~ 10 _

13~a_'b":: - ~o.:> ~(0) \}

".1..

g0(\ I?_)

17. (~t=~)~~m(0)\ ')~S 1''-

3. f(x) = (1)X-1(0, I) ,. -'.w.:J?+J -~-

4. f(x) = -3.+5 - 2

(01\)- 5 .-·1--2-

-;;L

\i-~j-5):J

(1)-- .:«:5. f(x) = '3 - 5 L4r -:::. J 6. f(x) = 4.. 3 ~:::o

-3~~}~)(_-~I ~)

lo;=iQ\l-', ~). _\ -s.

Cc \) -).)J

16. (m-2n ....J-)2121

'3mY)~I2. \ - 1/ z,

.{'X -(_~)I.+=v)5'" _ S

18. 5,"+2 - '. -:L f\\= 5 =-.~

22. ifX2,Vx+.JX 0'3;. -\P 3

~3 X -:: Xx\_

I A 7-31

=UlmJ\

I +--1-"3 "'t=! +- -3

,"2..~J_,...

-J__..!..2. v2..::Ja.::.l/1-.

\2. \ __

-+ to ;;_ 2._!..-3 tl-3 -:'''-3~

( 0\,)+- I ~).

(.II :l)

(0 )\)el-l-

\ (O/i.))'( \\qJ 1·1.

·1-(_( l__j \ .5')'

Name~ _ Dale, _ Period _ I A 7-41WORKSHEET - MORE EXPONENTIAL FUNCTIONS

Graph each exponential function.1. f(x) = fj" 2, f(x) = -ex - 1

3. f(x) = 2eX•1

.W

5. f(x) = iw)

'..... T-.li

. "

(0/ \)• -4-I

(0)-2)

(0,1).-.1 -~+!>

(0 I')-3 --d-( :»; -""I, ;.I) "'"

( ')~)_3 _.-;t

)~

(1 )X'2

7. f(x) =:4 -6

(0,\) iliilili

-+~ -t.~I-S)

(-I,~),.-\-'2 -I..

(\ )-.:i)

4. f(x) = e"··36

9. t{x) = 14xI

6. t(x) = _2(5)><+3

.,.

'V

8. t(X)=3Ixl

·w

10. t(x) = (i)"

I A 7-41

. .

Name __ Date __ Period

Solve the following equations for x.

WORKSHEET - EXPONENTIAL EQUATIONS

1.9X=310

J.2~)( 10

o z: ~;Z'X.::10[}:;5]

1-')~(1)x =55 3. 25-'2:

5 \5

5. 23 ·2x =8-x~TX -3)(.

~ :: ~3+)(: -3~3-::.-'-\'i-B3

7. 2x ·8-x =4xDX -31- ~c:7)'} • J ::.:zr/....)_'f.. ;;. 'f.0'\ =.;(

-;()(. = ~~o-r-o]x.-=:-D

8x•1 = 2.. 1 \2. 3 "'T"3~- ,...') -=2. \dj "2-=X-t3~- '-J

~-:!-~~ -tt

'?> 1 .c::-- a1- Ux-1

=64 y-:>.. ){-:? -v' ::o-(l.

:x .2--lf',3)(-,-,:_

~~-~~x+1 1"

6. 10 - 1000

)(..-\,,_It\D -:~rB-'2. :r l\3 1 2x ;:-::- 3

8, 9) = 81x+2

-~'1- L\'J.+t~ -:: 3_, L\ '" -;;-Lf'X. t <6-~~-=.~

~

--

-;)..e,

10. ex2 = ~3X ) . ....!...«"~ e2

» 3x"-:;>" ~e. ::-e ~~ "f...-;:; IX?-;~~-J_ X)(.;1-__ '3'J.. .....;L:;:- 0(:!-. _ ;)..) Cf. - 1) ::::.-n

2-

12 3x3

=~. ~8'1. ::; 3')..Y. ~ ~~ \~;;"-E:x::;:~~)<.~_~ -,0

~(_x.'2--:J}-:;' o

14. ~xr~=2:X~.l3,,;1)4 '5)(-3"" ":: ..:<" ~~ '0)(.-3t:'(X~ L~-C;()( -'O~""{ .. - ::.-0~~ "j..,~ )(~t

Write each expression in simplified form, using ~oSftivJational e~onents. I :{J )?-/:t. I15. (Sa.er2l3:: {_~ ~ ---'1 16. ~1112_9112)2

~~ It D-- ~ q - :sl-= \_%-j ",' ~~ :{3iPJ

I A 7-5 I9. ~4r·ex2 =....!...etfx r? e'! -3)(-_e

4X + 'i.Z-:::_~ ~?-.X +-1x.. ::. '0~ 'I- t-1):/ n

x-=:; 0 X~-l11. ~xl+1 =1~·;t Lf~ 'J. +)( if)( t-ti~.::::~@-t. .:: '" Co"h. -I-u )\ ~ "':."i--3~-4-=D 'j.- \

rl C)( - LtJL~:\-'l)::>"D.1..1;U )l-X 1:3. _ _4C2 -

X-I ;l..:2. -=-- J_

x-\ ':;?[i=)J

17. 2rr2l3(n6/3 - 3n~) 18. 1n"~(3n"3 -4n<l3)~n-ll3

n"I?>t3 nY:_ iff)'113)(3~-0

l3 Y1 ~- (p y)'\

I A 7-5 I

N

~_I_c:",,,,~~~~";1'N.c:"'N~~cO <0.,O.'<0

.... _

'-. to":--.0 _.

_ci, '"

.,j"'$.

~'"MMN

NI'"..,..11)'"~o.. N(/)-a::~ .._(/) ....~~

I A 7-61

Name _ Date _ Period

WORKSHEET - EXPONENTIAL APPLICATIONS1. A radioactive sample decreases by 25% each week.a) If you begin with 5 grams of the substance, givean equation for the amountremaining after t weeks. (' 15)04:

A(.!;)::-5 ~b) By graphing, find out when 2.5 grams of the substance remains. (This is the half-lifeof the suostance.) t.

;),.,S-=- '5 (,15)-t7 ~ I~ ~a_s

...

2. Suppose the annual rate of jnt!IDiQnaverages 3.80/9over the next 10 years. Thepresent cost of an oil change for your car is $23.95. Write a function for the cost of theoil change after t years and approximate the cost 10years from now.

:t.~):: ~olgt5( \'O~<i»f1 (\D) =t5 3tfl i<g

3. The city of Baltimore has been declin..!.!:!l!in population for the last 10 years. In theyear 2000, the population was 651,000 and declining at a rate of 1.2% per year.a) Give a formula for the population of Baltimore as a function <?tthe years since 2000(use t = 0 for the year 2000). Pte\::.) ~ /.Q 51000 ( ,~&)b) What is the predicted population in the year 2006? (Round to nearest whole number)

fH..Co') t:&5lC60 (. q~~)(P z: (.pD 561.l4. Radioactive lodine,.I'3', used to test for thyroid problems, has a half-life of 8 days.a) If you start with 20.g of radiollctiV~qdine, write a function for the grams of ,'31 left

after t days. f\81-; bl0(~ ) 1~b) How much would remain after 5 days?S

A(5):- d.o( 1-) 11.= J~. q1

I)

I A 7-61

5. Xenon gas, Xe'33, is used in medical imaging to study blood flow in the heart andbrain. When breathed, it is quickly absorbed into the bloodstream, and is graduallyeliminated from the body through exhalation so that there is half as much in the bodyafter 5 minutes. If the patient originally absorbs 3 mL of Xe'33, write the function for theamount of Xenon' left in the body after t minutes. How much would be left after 12

minutes? ~)c, '3 (~ )~_ " 5~<6

6. Write the function and find the amounts that result from each investment.a) $1200 invested at 4% compounded ~ after a period of 3 years.

A= \;tnt) 6+ ~)~. 3J135Q, f':jb) $5000 invested at 8% compounded monthly for 2% years .

. 1"><0.. '~' ~·&41 <"') QPt ::-5Db6 ( t -r ~ J -=- (0 t ou I I 1cJc) $750 invested at 6.25% compounded <w!y for 5 years.

/ .D~\g~6·~A-:. 750 l 1+ "Ole$') -::-10;).5, (D•

7. Write the function and find the principal needed to obtain each amount.a) To get $1000 aftef 2 years at 6% compounded daily. k

. ~\;~~~I oov-= 1/ ( I+ ,~ltS' ) ::- CZ8 ~ .Gf3

b) To get $10,000 after 5 years at 725% compounded quarterly.

r, . ()71.S"" )'i.9 I/DODO -= r(I t Lf z: &qg ,Ql

8. Joanne has just inherited an diamond ring appraised at $3000. Suppose diamondsappr~iate in value at a rate of 9% anoually.a) Write a function for the value of the diamond t years from now.

Pi ( -t)::: 30bD ( I.Cf1}bb) Find A(-10) and explain the meaning of the amount.-Ie>Pr (-ID) -=. ~()OO( I .0<1) sz: / 2~I. ;)._~

W'r'td" th~ t\io..m~ r \ ~ tJ-Y;...S~ fu \0 '-j.(ljJ., fS lA..':f .

·~

9. Average salaries of accountants are based on the number of years of experience.The function for the average salary with t years of experience is

A(l) = 42.000(1.084)'

b) What is the entry level average salary? H2&Q)(Entry level is with no experience.) '1

~ '-i2()C)O1

c) What would the salary be after 10 years?

() Cflf) O~ (11

d) When could an accountant expect to earn$150.000?

1le ~(5

REVIEW. (Non-calculator)Gra~

~ »: /' ./' /"

/: , r -'

'"'""'~

" " ~,""", 0 "~ ~".-

J

,;

11. f(x) = _.!.(4)X+2 - 32

I A 7-61

(0 )\")-I-S

(5)1)

(0 ) l') II'J .... --,.... ").:

-"b\(:~ )-3,5)\

(\)4)\-~ .-1--~~

-()(.~5)12. f(x)=e~x

Solve.

14. 93x -sr? =27

314'f. -'1:1' 3- '3 :;3~~ - 33 ~3.2.X :;;3

f]• I

'",

--------------------------------~~

'Goeslhrou(4.147)

.<;72x :.J,. ~

15. (iJ =12Sx '4~;2,

-leY· _ 7:,," +;L~ :::;:t

~J

'.

LQ ~ z: l~ t-;l

-1 ~_--::-~l

E,-M

a) What is the annual percentage increase in salary?

~ I Lf/u

,'1.1.>11

\

I'~

i'E

I A 7-61

~§.,N

t;l~"'~<it'"..5:.o~....IeE'-",1f.~:o~.n~'"f~~",for.

~N':cM·U;.:Q~j!.o~~~~Q.~

~$,<;1~.:g~&5 :o~~,C') uM';~'co(j)C-;t---"'~~"E.,.,.._:mr:i ~0) ~~',.o·lt),....~:.~,tri~~-~ ..~.q._"'O~ ().

.. "';:::.~,(hm '~ .~~s .'~.li!-C(":Ou

EJ r A 7-7 I5. The number of bacteria present in a culture at timE1t = 0 is 1000. The bacteria have acontinuous growth rate of 2.25%.

Name __ PeriodDate __

WORKSHEET - EXPONENTIAL APPLICATIONS 2a) Write the function to model the growth of the bacteria at time t in hours.

A-:::: IDDD e: e>J,;;.S-Cb) When will the number of bacteria double? (Solve by graphing.)

~.:;{ rw-u,fSc) When will the number of bacteria reach 10,000?

103 ~6. Strontium-90 is a radioactive material that decays according to the lawA(t) = Ao e·O•02404t, where t is in terms of years. How much of a 10 g sample would be leftafter 15 years?

( -, - ,D?. i.f4 (,0)-A IS):: IDe .: ( I ~ 3>

For each problem write the function.1. Wrile each function and determine the balance for an investment of $1500 after 3 yearsinvested at 8%

~ ,2, (.~) ~IQ 5a) compounded monthly? F\:::. 1500U.}-" )2.) s: \ 10 ,?:::J.p

. I ~)3l#~('~) = a t . 0 t')b) compounded daily? po. -:: IVOD L \ + 'a>leti'" l-ID"iJ I o«c) ~pounded continuously?" ~ ':" \ ~C:D e~l.D<&) ::. Iqol.R .,.~72. John inv~ts $2000 in a bond fund that pays 4.75% compounded ~rly. His friendHenry inve.sts $2000 in a Certificate of Deposit (CD) that pays 4%% compo~undedcontinuously. Who has more mon~ after 20 years? - J """('

f\.-;. /)"Dq"O ( I ~. OLt~ 5 y+tz,..O) z: '514- ~ ,~ 'P ~ it f)WfJa'QoD e,.f).O' .O~ :: Lf1l4 I d.--I . 7. Radioactive radium has a .half-life of 1620 years. If 25 grams of radioactive radium

were present at t = 0, how many grams would be present after 1000 years?

fo ~ 45 (_i)~~ f_v,~q,3. If you need $25,000 six years from now, what is the minimum amount of money youneed to deposit into an.account that pays 5% interest compounded continuously?

R ~~='? e'D5{lp}

t?-.=--\ ~-s;t-. D-I ~-;-;l. ~ ~

'" -

.,.

8. A $20,000 car depreciates at the rate of 20% per year. Write a function for the value ofthe car after t years. Sara plans to keep the car until she graduates from college in fouryears. What should the car be worth at that time?. ., ;'1

tJj:c1 0000 (, 1» _:-<{; \9 d-

4. The population of a town increases according to the model P(t) = 2500eO.02931,where t isthe time in years (I" = 0 represents the year 2000)., ,a) Whal was the population of the town in the year 2000? ~ '000

,H

b) Estimate of the population in the years 2015 and 202510 the nearest person.

t::;J5'3~-8Dj ANSWERS: 1. a) $1905.36 b) $1906.82 c) $1906.81 2. John: $5142.56 Henry: $4919.21 3. $18520.46

4. a) 2500 b) 3880, 5201 5. b) 30.801 hours c) 102.331 hOurs 6.6.9359 1.16.291g 6. $6192

t,::;]S 5zu»

'-.'.\ ..... \