Algebra E oi0vy9l XKguTtTaI ssofvtmwjafrqet BL_LvCJ.e g ]AMlUlQ SrTiRgfhttcsd NrwessFeArnvVe^df. THT0: Eponentials Simplif. Your answer should contain onl positive eponents. ) ) k k 0k k k 0k ) n n 0 90 n 0 n n 7) m m - m 7 m m m 9 9) ( )- 09 ) ( p - ) 79 79 p 0 7 p 9 p ) ( ) p ) b b 0 b b b ) n n - n 0 n n n ) k k - 0k 7 9k k k ) r r - r r r r ) ( n 0 )- n n ) ( m - )0 79m ) ( 0 ) m m 777 0 777 ) ( b )- b 0 b b 0 0 ) ( p ) p 79 p p Worksheet b Kuta Software LLC b 0 v mn0fi9a AKHuLtkaa YSZoJfQtsweaVrae dlflwcw.b P oaolqlw eryitgeh^tcsu or]e\snelrhvbeodm.s -- d SMtaddseN pw\imthd fiknpfcivnsijt[en aaalvgbepbrriav ae.
7) n n - n n n ) - 9) k- k ) n n k k k k n n n n 0) - ) - 9 ) v v - v ) ( - ) v v 0 7) ( - - ) - 9 7 ) v- v - v v ) n ( n ) v 9 v n n 0 n n ) () 0 9) M P0\q9e tkwuktba` USdoMfztTwfaGrveJ tlrlrcb. f nadluly trhiagdhrtrst UrUefsmegrYvXegdb.R Z tmjaldqeh Gw\iethp UI\nMfYiJn]iNtker eael\g_egbprda[ im. -- 0) m - m m - 0m 7 m 7 m m Worksheet b Kuta Software LLC
) p - p p - p p p p ) - ) ) 7) 9) n 0 ( n )- n n n 7 n a ( a ) a a ( 0 ) a a p p - ( p 0 )- p 9 p p p 0 ) ( ) - ) 0 n 0 (n) 0 n n n ( ) b- b b )- ( b )- b b b b 0 ( ( k ) - )0 k 0) 0 ( k ) k k Simplif. ) 7 7 7 ) 7 ) ) -- t j]0z_9o EKNuJtXaS \SBoGfFtHwKaKrbeL \LALcCs.l S [AKlXl PrRiGgZhItksJ [rkeosuexrcvgeqd^.i \ M^apdVei Qw[iCtWhX ticnmfhivnaiktzee NAlTgeelbPrHaQ Vk. Worksheet b Kuta Software LLC
) a a a a a 7) m m 7 m m m 9) 0 ) - 0 - ) m m m 90 ) ) a a 7a 7 a a ) n n n 7 n n n 0) 0 7 ) - 0 - ) r r 9r r ) 9 7) - - 9 9) 9 Eponential Functions ) What is the general form of an eponential function? ) 9 0) - - - f () = f () = f () = a f () = ab [ TF0Sb9N mkjuvtja] SNoLf`twbaUrGe` _LuLZCj.U R [A_lplR ureibghhytts` grtens_ewrev^ecdb.p w qmlafdneo ^wqiethhz ]IWnjfwiYnMiatOeX XASlZgJeCbtrwaZ [u. -- Worksheet b Kuta Software LLC
) What is an alternate form for an eponential equation? f () = f () = a f () = a( + r) f () = ) What is the difference between a linear function and an eponential function? Choose all that appl. Linear functions increase b the same sum; eponential functions b the same multiple Linear functions grow faster than eponential functions. Linear functions create a line; eponential functions create a curve Eponential functions have the variable as an eponent Identif the functions as representing eponential growth or eponential deca. ) f () = ( ) ) f () = - ( ) Eponential Deca Eponential Growth ) f () = Eponential Deca Eponential Growth Eponential Growth Eponential Deca 7) f () = ( 7 ) Eponential Deca Eponential Growth ) 0 9) 0 - - - - Eponential Growth Eponential Deca - - - - Eponential Growth Eponential Deca ` tz0an9u EKwuhtAaf msvobfztfwia_rqem RL]LWCg.h Q `AFlblU `r_iagghatvsf r^emsue_rvwekda.o S omawdceq gw^idtdhm MIanAfXiBn_ietheT eaalng[eabzrbay bz. -- Worksheet b Kuta Software LLC
70) 0 7) 0 - - - - Eponential Deca Eponential Growth - - - - Eponential Growth Eponential Deca 7) The interest on a back account increases b.% annuall. Eponential Deca Eponential Growth 7) The value of a car depreciates b 0% per ear. Eponential Growth Eponential Deca Use the scenario to answer questions #7-7 A new car is bought for $,000. The car is epected to depreciate b about % per ear. 7) Write an eponential function, V, that represents the value of the car after t ears. V(t) = 000 0. V(t) = 000( - 0.) V(t) = 000 V(t) = 000( + 0.) 7) After ears, approimatel how much is the car worth? Round to the nearest dollar. $, $9,7 $7,0 $,000 Use the scenario to answer questions #77-0 7) Is the car worth nothing after ears? I wouldn't want it anmore. Yes Almost No 77) After how man ears is the car worth less than $,000? ears ears 0 ears ears A population of bacteria doubles ever week. Originall, there were 0 bacteria. 7) A scientist wants to have at least 000 bacteria for a stud she's doing. How long will it take the population to grow that much? weeks week months weeks _ pl0bb9a MKlu]t[ar zsqowftxwha`rset VLoL^C[.b r BArlFlR frdixgthats irmexsceqrdv[ebd\.o L bmjadiew owmiothhu fion\frijnyi_teez daflhgsejbsrzab LL. -- 79) Write an eponential function, P, that describes the bacteria population after w weeks. P(w) = 0 P(w) = 0 P(w) = 0 + P(w) = 0 Worksheet b Kuta Software LLC
0) After weeks, how man bacteria are there? 7 bacteria 0 bacteria 00 bacteria 00 bacteria ) After weeks, how man bacteria are there? 00 bacteria 00 bacteria 0 bacteria 7 bacteria Use the scenario to answer questions #77-0 Two high school districts have studied enrollement trends and made the following predictions. South High School currentl has 70 students and epects to increase b % per ear. North High School currentl has 90 students and epects to increase b students per ear. ) Write a function, S, that describes the population of South High School after ears. S() = 90( + 0.) S() = 70( + 0.0) S() = 70 + 0 S() = 90 + ) Write a function, N, that describes the population of North High School after ears. N() = 70 + N() = 90( + 0.) N() = 70( + 0.0) N() = 90 + ) What is the population of both schools after two ears? South: 7. students; North: 00 students South: 7 students; North: 0 students South: 7 students; North: 00 students South: 7. students; North: 0 students ) What is the population of both schools after four ears? South: 7 students; North: 00 students South: 90 students; North: 0 students South: 90 students; North: 00 students South: 90.9 students; North: 00 students ) After how man ears is the population of South High School greater than that of North High School? B how much? ears; 0 students 7 ears; 9 students It's never bigger ears; students 7) After ears, which school has the higher population? What is the difference? The're the same South, b students North, b students South, b 9 students Identif the domain, the range, and the horizontal asmptote of the function. ) f () = 00. Domain: (-, ); Range: (-, ); Horizontal Asmptote: = 0 Domain: (-, ); Range: (0, ); Horizontal Asmptote: = Domain: (0, ); Range: (-, ); Horizontal Asmptote: none Domain: (-, ); Range: (0, ); Horizontal Asmptote: = 0 ^ gu0xp9y ukmufthav SRoffStswKaBrfeO NLdLvCj.H e DAHlolB \ricgihqtism ZrPeEsSeFrCvreHdD.c w UMVaadZeQ kwpiktlhz PI]ndfqiVnCiMtKeJ HApl[gBeXbIraW Kp. -7- Worksheet b Kuta Software LLC
Sketch the graph of each function. 9) f () = 0 90) f () = 0 - - - 0 - - - 0 - - - 0 - - - 0 - - - 0 - - - 0 - - - - - - j [a0og9e ekouitmab ES[oMfGtdwJa]roeo JLaLuCM.k h HAzlClw [rtikgvh\tlsb Rree\sAeNrbv_ebdS.l s CMLa_dee fwkiutthn JITnXflifnuiot]e` dail]gdeibqrbaq \. -- Worksheet b Kuta Software LLC
9) f () = 0 9) f () = 0 - - - 0 - - - 0 - - - 0 - - - 0 - - - 0 - - - 0 - - - - - - S dt0jw9a rkruktuaz HS_o_fWtXwCaSrOep cldl\cf.e s JAglRlN KrIizg]h_tJsk RrheEsUeMrfvievdM.[ d OM[a\dDeK `wvigtchf WIhnnfXimnpiStkeJ QA]lIgBe\bHrwaq X^. -9- Worksheet b Kuta Software LLC
9) f () = ( ) 9) f () = ( ) 0 0 - - - 0 - - - 0 - - - 0 - - - 0 - - - 0 - - - 0 - - - - - - Q cw0vh9f PKSuUtVa ls\oxfdtqwoavrde[ HL[LgCd.` t Aqlli \rzipgphdtmse CrelstePrnv\ezdc.\ b fmwajdgeh `wmigthd TI[ngfRiqnmittFeA iasleg[evborraz jr. -- Worksheet b Kuta Software LLC
9) f () = ( ) 9) f () = ( ) 0 0 - - - 0 - - - 0 - - - 0 - - - 0 - - - 0 - - - 0 - - - - - - j Ld0uT9l ZKauztaau vsqodfgtwlaortee PLvLgC^.b j vawlrlf mrficgvhxtssu jrtewsfeirqvvemdj.d R RMLaCdPeB VwtiZtChe \IVnkfVitneiItWew gajlkgjekbrnar bu. -- Worksheet b Kuta Software LLC
97) f () = - 0 - - - 0 - - - - - - - 9) f () = + - - - - - - - - - - - - 0 - - - b jf0ta9a vkdugtias ^SrowfQtIwqafreeF [LrL]CA.d n naclplk \rkiigfh_tjsm [rvevswecrsvaeidx.o [ emfatdne` `wdiltkhr qiknjfrinnfimteew raslvg[edbwrmaz ry. -- Worksheet b Kuta Software LLC
99) f () = + 0 - - - - 0 - - - 0 0) f () = ( - ) 0 - - - - - - - - - - 0 - - - - - - - - - - - b WZ0`k9b [KWuztTaS `SwopfvtZwna^rReL ^L^LtCR.g s saolxlr qrilguhrtest jraeaspevrfvwefdu.h X JMBaAdmeU VwliKtQhX cifnff[idnfibtaes RALlbg\eUbUrkaP lq. -- Worksheet b Kuta Software LLC