15.) a 5. a 24.) 1 23.) 3. Determine if the series has a sum. If the series has a sum, evaluate the series described ) 35.)

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1 Uit Assigmts Nam: Assigmt. Gomtric Squcs Fid th commo ratio, th t two trms, ad th plicit formula..),,,.),,,,.),,,.),,,,.),,,,.),,,.),,,.),,,,.),,,,... 0.),,,,....),,,....),,,... Fid ad graph th first trms..) a.) a.) a.) a.) a.) a.) a 0.).) a.) a.) a Dtrmi if th sris has a sum. If th sris has a sum, valuat th sris dscribd. a 00 a.).).) m.).) y m p.) y 0.) p.) k.).).).) g g.) p h p.) Makrs of Japas swords i th 00s rpatdly foldd ad hammrd th mtal to form layrs. Th foldig procss icrasd th strgth of th sword sic aftr th first fold thr would b two layrs, aftr th scod fold thr would b four layrs, ad so o. Writ a rul for th gomtric squc that rprsts th umbr of layrs i trms of th umbr of folds. How may layrs of mtal would a sword hav aftr si folds?.) Julia ss a w bad at a cocrt. H tts th lik for th bad s wbsit to fiv of his frids. Thy ach forward th lik to fiv of thir frids. Th lik is forwardd agai usig th sam pattr. How may popl will rciv th lik o th ighth roud of tts? How may total popl will hav rcivd th lik o th ighth roud?.) Sara rcivs a jok i a -mail that asks hr to forward it to four of hr frids or sh will hav yars of bad luck. Sh forwards it, ad th ach of hr frids forwards it to four of thir frids, ad so o. If th pattr cotius, how may popl will rciv th -mail o th ith roud of forwardig? How may total popl will hav rcivd th -mail o th ith roud? 0.) Mirada arrags i rows of domios so that aftr sh kocks ovr th first o, ach domio kocks ovr two mor domios wh it falls. How may domios ar i th last row? How may total domios will Mirada us?.) Da is makig a family tr as a birthday gift for his fathr. H was abl to trac may gratios. If da could trac his family back 0 gratios, startig with his parts, how may acstors would thr b?.) Th umbr of poits dd to pass a lvl i a vido gam doubls with ach lvl. If 0 poits ar dd to pass lvl o, how may poits will b dd to pass lvl t? Oc you pass lvl t, how poits total will you hav accumulatd? h

2 Assigmt. Epotial Growth Graph fuctio. Idtify th trasformatios, domai, rag, ad asymptot..) f.) f.) f.) f.) f.) f.) f.) f.) f 0.) f.) f.) f.) f.) f.) I 000, th populatio of a city was about.0 millio. Durig th t yars, th populatio icrasd by about.0% ach yar. Writ a potial growth fuctio modlig th populatio P (i millios) t yars aftr 000. What is th city s populatio i 0?.) Th umbr y of duckwd frods i a pod icrass by % ach yar. Writ a potial growth fuctio modlig th umbr of duckwd frods aftr t yars if th pod iitially startd off with 0 frods. How may duckwd frods ar i th pod aftr yars?.) Jaso rad that i th avrag rsidtial vhicl travld about 0,00 mils, which icrasd by about.% pr yar through 00. Writ a fuctio for th avrag milag, m(t), as a fuctio of t, th tim i yars sic. Us th fuctio to prdict th milag of Jaso s vhicl i th yar 00..) You hav ihritd lad that was purchasd for $0,000 i 0. Th valu V of th lad icrasd by approimatly % pr yar. Writ a potial modl for th valu of th lad t yars aftr 0. What is th approimat valu of th lad i 0?.) From to, th avrag umbr of trasistors o a computr chip ca b modld by 00. t whr t is th umbr of yars sic. What was th iitial amout of trasistors i? By what prctag did th umbr of trasistors icras ach yar? Us th modl to stimat th umbr of trasistors o a computr chip i. 0.) Th valu V of a atiqu tabl t yars aftr it is purchasd ca b modld by th fuctio V. 0 t. What was th valu of th tabl wh it was purchasd? How much did th valu icras ach yar? What will th valu of th tabl b 0 yars aftr it was purchasd? Assigmt. Epotial Dcay Idtify th fuctio as ithr potial growth or potial dcay. Graph fuctio. Idtify th trasformatios, domai, rag, ad asymptot..) f.) f.) f.) f.) f.) f.) f.) f.) f.) f 0.) f.) f.) f.) f.) f.) f.) f.) f

3 . Cotiud.) You bought a computr for $,00. Th valu V of th computr dcrass by about 0% aually. Writ a potial dcay modl for th valu of th computr t yars aftr it is purchasd. What will th valu of th computr b aftr yars? 0.) A bottl of Hour Ergy cotais 00 milligrams of caffi. Each hour h, th amout of c caffi i your systm dcrass by about %. Writ a potial dcay fuctio that modls th amout of caffi i your systm. How much caffi will b i your systm aftr hours?.) Th attdac for a basktball tam dclid at a rat of % pr gam throughout th losig saso. If,00 popl attdd th first gam, writ a fuctio modlig th umbr of popl P attdig aftr g gams. How may popl attdd th th gam?.) You tak a milligram dosag of ibuprof. Durig ach subsqut hours, th amout of mdicatio i your bloodstram dcrass by about % ach hour. Writ a potial dcay fuctio givig th amout y (i milligrams) of ibuprof i your bloodstram t hours aftr th iitial dos. How much mdicatio will b i your bloodstram aftr hours?.) Th valu of a moutai bik Y (i dollars) ca b approimatd by th modl Y 000. t, whr t is th umbr of yars sic th bik was w. What was th iitial valu of th bik? By how much dos th valu of th bik dcras ach yar? What will th valu of th bik b aftr si yars?.) Th valu V(t) of your ivstmt i a crtai stock aftr t yars ca b modld by th fuctio V t 000. t. How much moy was iitially ivstd i th stock? By what amout did th valu of th stock chag ach yar? Assigmt. Eulr s Numbr Graph fuctio. Idtify th trasformatios, domai, rag, ad asymptot..) f.) f.) f.) f.) f.) f.) f 0.) f 0..) A amout of $,000 is ivstd i a accout arig % compoud itrst. Fid th valu of th accout aftr yars if th itrst is compoudd a) quartrly, b) smiaually, c) mothly, ad d) cotiuously. 0.) A ivstmt i a accout with itrst compoudd cotiuously ca b modld by th fuctio A 0 whr A is th amout of th ivstmt aftr t yars. How much was iitially ivstd i th accout? What is th prct rat? What will th valu of th accout b aftr 0 yars?.) Ivstmt accouts for a hous ad ducatio ar aual itrst compoudd cotiuously. Th balac H (i dollars) of th hous fud aftr t yars ca b modld by 0.0t H. Th graph to th right shows th balac i th ducatio fud ovr tim. Which accout has th gratr pricipal ivstmt? Eplai your aswr. 0.0t Simplify th followig prssios..).) 0.).).) 0.) 0 0.).)

4 Assigmt. Logarithms Rwrit th followig i potial form..).) 0.).) 000.) l. 0 Rwrit th followig i arithmic form..).).)..) ) 0 Evaluat th followig arithms without a calculator..).).) 00.).).).).).) 0.).).).) /.) l.).).) 0.).) l 0.) 000 Assigmt. Proprtis of Logarithms Us th chag of bas formula to valuat th followig arithms..).).).) Epad ach of th arithms. Mak sur your aswrs ar compltly simplifid..) y.) ab.) b 0.) l.) q a.) b 0.).) l m p.) m.) a c.) bd.) yz gh.) 00 j.) y.) y z Cods ach of th prssios to a sigl arithm. Mak sur your aswrs ar compltly simplifid. 0.) y.) b.) m a.) 0.).. 0.) a b c.) y.) 0.) l 0 l l.) 0.) p. ) h g m

5 Assigmt. Solvig Epotial Equatios Solv ach quatio..).).).) m m.) a a.).) ).) 0 0.) y 0 0.).) 0 00.) m.).).) 00.) 0.).) 0 p 0.) 0 g0.).) 0 0.) 0.) 0.) Th quatio y.. t modls th populatio of th U.S. i millios from 0 to 0, whr t is th umbr of dcads sic 0 ad y is th populatio i millios. How may dcads aftr 0 did th populatio rach. millio?.) Th valu A of a ivstmt i a accout that compouds itrst cotiuously ca b modld by th fuctio A How will it tak for th ivstmt to doubl its valu?.) Th valu of a car that was purchasd i th yar 000 for $,000 dprciats by about % pr yar. Writ a modl givig th valu V of th car t yars aftr 000. What will th valu of th car b i 0? Wh will th valu of th car b $,000?.) I 0, th populatio of rabbits i a forst was about,000. Durig th t 0 yars, th populatio icrasd by about % ach yar. Writ a fuctio modlig th populatio, P, t yars aftr 0. What is th populatio i 00? Wh will th populatio rach,000?.) Gorg has dpositd $0,000 i a accout that pays % aual itrst compoudd cotiuously. Writ a 0.0t 000 whr t is th umbr of yars of ivstmt. What is th balac of th accout aftr yars? quatio for th balac A of th accout aftr t yars. What is th balac aftr 0 yars? How will it tak for his ivstmt to tripl its valu? Assigmt. Solvig Logarithmic Equatios.).) m 0 m.) y 0 y.) l g l g.).) 0.) y.) l.) 0.).) m.).) 0.).) 0.).).) l 0 l l.) 0.).) 0

6 Assigmt. Ivrss of Epotial/Logarithmic Fuctios Fid th ivrs of ach fuctio..) f.) f.) f.) f 0.) f.) f.) f.) f.) 0.) f.) f l.) f f Vrify if th fuctios ar ivrss by compositio..) f ad g.) f ad g l.) f l ad g.) f ad g /.) f ad g 0.) f ad g Assigmt.0 Graphig Logarithmic Fuctios Graph ach fuctio. Idtify th trasformatios, domai, rag, ad asymptot..) f.) f.) f.) f.) f.) f.) f l.) f.) 0.) f.) f f.) f.) f.) f Match th fuctio with th corrct graph..) f.) f.) f