Unit 2 Exponents Study Guide

Transcription

1 Unit Eponents Stud Guide 7. Integer Eponents Prt : Zero Eponents Algeric Definition: 0 where cn e n non-zero vlue 0 ecuse 0 rised to n power less thn or equl to zero is n undefined vlue. Eple: 0 If ou look t the chrt, when eponents decrese one in the tle of vlues, the vlue is divided, so 0 is equl to. Eercises: Siplif Power Vlue = = - =. 0 6 (0) = undefined Prt : Negtive Eponents Algeric Definition: Eples: n where cn e n non-zero n vlue. 0 ecuse division 0 is n undefined vlue. ( ) ( )*( )*( )*( ) 6 * * *** * 6 6

2 Eercises: Siplif using positive eponents onl.. =. c c =. = 6. = 7. Powers of 0 nd Scientific Nottion Prt : Multipling Powers of 0 Eple: 6.*0 6.*00,000 6,0,000.*0.* 0.* Positive Integer Eponent: if the eponent is positive integer, n, ove the decil n nuer of spces to the right Negtive Integer Eponent: if the eponent is negtive integer, n, ove the decil n nuer of spces to the left Eercises: Find the vlue of ech epression = 8,0,000 = *0.

3 Prt : Scientific Nottion Eple: A nuer written in scientific nottion hs two prts. Prt One hs decil tht is greter thn or equl to one nd less thn ten. Prt Two is power of 0.,6,6, =,6,6, =. 0 decil spces fter the decil = positive power of = = spces efore the decil decil = negtive power of 0 Eercises: Write using Scientific Nottion.. 8,,6,,6, 00 = = Multipliction Properties of Eponents Propert Algeric Definition Eple Product of Powers n n 9 Power of Product 9 n n Power of Power

4 Eples: 8 * * 6 6 Eercises: Siplif full.. c c. * * = 7 6 c =. ) ( = 6 7. Division Properties of Eponents Propert Algeric Definition Eples Quotient of Powers n n k k k k 8 8 Power of Quotient

5 Eercises: Siplif full. 8 6 z.. 6 z z 6 6 = = n n n 7 8 = 9 = n. Eponentil Functions Eercises: Prt : Evluting Eponentil Functions Algeric Definition: f, where 0, nd Eple: The function, f, odels n insect popultion fter nuer of ds. Wht will the popultion e fter ds? ***** 86 f insects fter ds. The function, f 00(0.99), odels pririe dog popultion fter nuer of ers. How n pririe dogs will there e in 8 ers? 8 f 8 00(0.99) = pproitel pririe dogs

6 . The function, f , odels the width of photogrph in inches fter it hs een reduced % nuer of ties. Wht is the width of the photogrph fter it hs een reduced ties? f 80.7 = pproitel.7 inches Prt : Identifing n Eponentil Function Eple: Deterine if the ordered pirs represent n eponentil function: { ( -, ¾ ), ( -, ½ ), ( 0, ), (, 6 ), (, ) } Plce the ordered pirs in tle of vlues. **Eponentil functions hve constnt rtios** f the vlues re incresing ech tie the vlues re eing ultiplied ech tie There is constnt rtio etween vlues nd vlues; therefore, this tle represents n eponentil function. Eercises: Deterine if the ordered pirs represent n eponentil function. Eplin wh or wh not.. { ( -, -9 ), (, 9 ), (, 7 ), (, ) } No, there is constnt increse in the -vlues, ut not constnt rtio etween vlues.. { ( -, ), ( -, ), ( 0, ), (, ½ ) } Yes, there is constnt increse in the -vlues nd constnt rtio of the -vlues. The re eing ultiplied ½.

7 Prt : Grphing Eponentil Functions Eple: Grph: Mke tle of vlues nd grph the points - /6 - / 0 8 Eercises: Grph the following...

8 .. (0.). Eponentil Growth nd Dec Prt : Eponentil Growth An eponentil growth function hs the for, t r, where: = the finl/totl ount = originl ount which is greter thn 0 r = rte of growth, percentge, written in decil for t = tie Eple: The originl vlue of pinting is $00, nd the vlue increses 9% ech er. Write n eponentil growth function to represent this sitution. Find the vlue of the pinting in ers. = unknown t this tie = $00 r = 9% = 0.09 t = ers 00( 0.09) 00(.09) $07.

9 Eercises:. In 000, sculpture ws worth $00. Its vlue hs een incresing 8% per er. Write n eponentil function to represent the totl vlue of the sculpture. Find the vlue of the sculpture in (.08) pproitel $90.7 Prt : Copound Interest r A Copound Interest function hs the for, A P, where: n A = the Blnce fter t ers P = Principl / originl ount r = Annul interest rte, written in decil for n = nuer of ties interest is copounded per er t = tie in ers Eple: Invest $000 t n interest rte of % copounded qurterl for ers nt A = unknown t this tie P = $000 r = % = 0.0 n = qurterl = ties t = ers 0.0 A 000 A 000(.007) A * Eercises: Find the lnce:. $8,000 invested t rte of.% copounded nnull for 6 ers 6* 0.0 A A $ $00 invested t rte of.% copounded qurterl for ers * 0.0 A 00 00(.0087) A $79.9 6

10 . $000 invested t rte of % copounded onthl for 8 ers Prt : Eponentil Dec 8* 0.0 A (.00) A $08.7 An eponentil dec function hs the for, t r, where: = the finl/totl ount = originl ount tht is greter thn 0 r = rte of dec, percentge, written in decil for t = tie Eple: The popultion of town is decresing t rte of % per er. In 000, there were 00 people. Write n eponentil dec function to odel this sitution. Find the popultion of the town in = unknown t this tie = 00 r = % = 0.0 t = 0 ers 00( 0.0) 00(0.99) people Eercises:. The fish popultion in stre is decresing t rte of % per er. The originl popultion ws 8,000 fish. Write n eponentil dec function to odel this sitution. Find the totl fish popultion fter 7 ers ( 0.0) 8000(.97) = pproitel 8,78 fish Prt : Hlf Life A Hlf Life function hs the for, t A P 0., where: A = finl ount P = originl ount t = nuer of hlf lives in given tie period

11 Eple: Flourine-0 hs hlf life of seconds. Find the ount of Flourine-0 left fro 0-gr sple fter seconds. A = unknown t this tie P = 0 grs t = (/) = hlf lives A 0(0.) A. grs Eercises:. Find the ount of Flourine-0 left fro 0-gr sple fter inutes. Round our nswer to the nerest hundredth. **Reeer Flourine-0 hs hlf life of 0 seconds ** A = 0(.) 6 = 0.6 grs. Cesiu-7 hs hlf life of 0 ers. Find the ount of Cesiu-7 left fro 00 illigr sple fter 80 ers. A = 00(.) 6 =.6 g. Bisuth-0 hs hlf life of ds. Find the ount of Bisuth-0 left fro 00 gr sple fter weeks. ( HINT: Chnge weeks to ds) A = 00(.) 7 = 0.78 g