UNIT #5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS

Transcription

1 Answr Ky Nam: Da: UNIT # EXPONENTIAL AND LOGARITHMIC FUNCTIONS Par I Qusions. Th prssion is quivaln o () () Th ponnial funcion y 6 could rwrin as y () y y 6 () y y (). Th prssion a is quivaln o which of h following as long as a 0? a () a () a a a a a a. Which of h following would giv h sam rsul as? 8 () () 8 6. For h funcion f 7, which of h following rprsns is y-inrcp? 7 () () 7 f ()

2 6. Which of h following could h quaion of h graph shown low? y 00. () y 0.7 () y. y. In h gnral ponnial quaion y a, a rprsns h y- inrcp and rprsns h muliplicaiv growh or dcay consan. Sinc h y-inrcp is lss han, w could only hav choic () or (). Bu, sinc h ponnial dcrass, 0, hus i mus choic (). () 7. Slcd valus of an ponnial funcion of h form y a hundrdh, which of h following rprsns h valu of? ar shown low. To h nars. ().78 () y ? 8. Which of h following valus of solvs: () () () 9. In rms of h unknown consan a, which of h following valus of solvs: 7 a () 8 a () a a a a 6 a 6a 6 a 6a 8 a a 8 a 9 a? () 0. A populaion of frui flis is incrasing a a ra of.% pr hour. If h populaion had an original siz of 0 flis, hn which of h following is is siz afr on day? 798 () ()

3 . Th war lvl in a draining rsrvoir is changing such ha h dph of war dcrass y 7.% pr hour. If h war sars a a dph of f, hn which of h following funcions proprly modls h dph, d, as a funcion of im,, in hours sinc i sard draining? d.07 () d 7. () d.9 d 9. 00% 7.% 9.% of h war rmains d 0.9 (). Th mpraur of a cooling liquid in a room hld a a consan 7 dgrs Fahrnhi can dscrid y h quaion F.97 7, whr F is h Fahrnhi mpraur and is h amoun of im i has n cooling, in minus. Which of h following was h original mpraur of h liquid whn i gan cooling? 7 () 0 () 07 F If a populaion grows a a consan ra of.8% pr yar, hn y wha prcn will i grow ovr h n 0 yars? % () % () 8% 9% Thus, sinc w ar mulipying y. pr 0 yars, h 0 yar incras is approimaly %. (). Th half-lif of a radioaciv marial is h amoun of im i aks for 0% of is radioaciviy o dcras. If a paricular marial has a half-lif of yars, hn wha prcn will rmain radioaciv afr 00 yars?.8% ().8% ().7% 8.7% Sinc w muliply y 0. vry yars, his mans w muliply y 0. vry yar. So, if w apply his for 00 yars w g: %. Which of h following is closs o h valu of log 0?.8 ().7 () (closs o 0). 8 ()

4 6. If 0 hn log is qual o () () log log 7. Givn h funcion f log 8 funcion? () 8 () 0, which of h following valus of is no in h domain of h Th argumn of h logarihm, 8, mus grar han zro () 8. Which of h following quaions is shown graphd on h grid low? y () y () ylog ylog This is a sandard logarihm graph, y log shifd unis o h righ. Thus, i mus : ylog () 9. Which of h following is quivaln o log () log log y log log log y log y () log log y y? y log log log y log log y log log y log log y log log y 0. If log. hn log? 0. ().6 ().78 0 log log log..6 ()

5 . If 7 hn log 7 () log. () log log log. log. log. (). If f hn which of h following valus of solvs h quaion 90 f?. ().8 () log 0.9 log 0. log 0.9 log 0. log0.. () log0.9 k. If a c 0 hn which of h following is h valu of asd on a, k, and c and h naural as? ln c k a () ln c ak c () ln ak ac k ln a k k k c c a c ln a k c ln ln a c k ln a c ln k a. If $00 is placd in a savings accoun ha arns a 6% nominal inrs compoundd monhly, hn which of h following rprsns h accoun s worh afr 0 yars? $ () $89. () $87.9 $ $ How many yars, o h nars nh, would i ak for an invsmn o doul if i is arning a coninuous compound inrs of.% pr yar? 7. yars (). yars () 9.8 yars. yars A P A P r.0 A P? P P ln ln.0 ln ln ()

6 k 6. If a liquid is cooling down according o h formula y8 and a h mpraur is y 7 hn which of h following is h valu of k o h nars hundrdh? 0.08 () 0.9 () k 8 7 k 8 7 k 8 6 k 6 8 k 6 6 ln ln ln 8 k 8 6 ln 8 k Th mpraur of a cooling liquid is givn y h funcion m T m 8 0.8, whr T rprsns h mpraur in dgrs Clsius and m rprsns h numr of minus, m 0, ha h liquid has n cooling. Which of h following rprsns a mpraur ha h liquid dos no rach as i cools down? () () 6 8 Th saring mpraur of h liquid is 8+ or 9 dgrs. Th room mpraur is dgrs. Th liquid will hi all mpraurs wn and 9, hus will no hi 6. () Fr Rspons Qusions 8. On h grid shown low, h graph of f is shown. (a) On h sam graph grid, cra an accura skch of his funcion s invrs, f.,, 0,, 0,,,,, 8 8, () Sa h quaion of y log f. (c) Sa h domain and rang of oh f and f. f f Domain: All ral numrs or Domain: 0 Rang: y 0 Rang: All ral numrs or

7 9. An ojc is slowing down such ha is spd is dcrasing ponnially. If afr sconds i is ravling a 8 f pr scond and afr sconds i is ravling a only f pr scond, hn find an quaion in h form y a for h spd, y, as a funcion of h numr of sconds,, ha hav passd. Find h quaion using algraic chniqus. Round oh a and o h nars hundrdh. Two poins ha li on h curv:, 8, a a 8 () a () 8 a a y can wrin as a in simpls form. Drmin h valu of a. Show how you arrivd a your answr. 0. Th prssion 6 a. If g 7 hn algraically drmin h soluion o h quaion g For h logarihmic funcion f log, plain why 0 is no in is domain. 0 log 0 log f I is impossil using ral numrs o valua his logarihm. A as of raisd o any ral numr will always giv a posiiv rsul. Thus, hr is no log and, hnc, 0 is oupu o h prssion no in h domain.

8 . For som as,, i is known ha valu of log 0. Eplain how you found your answr. log.8 and log 0.. For h sam as, drmin h log 0 log 8 log 8 log log log log log , whr w rprsns h worh in dollars and rprsns h numr of yars sinc h principal was dposid ino h accoun. Algraically drmin h numr of yars, o h nars quarr of a yar, i aks for h accoun o worh $00.. A ank accoun s worh can modld using h formula w log log log log.7... log log Why dos i mak sns o round your answr o h nars quarr of a yar? Basd on h srucur of h funcion, i is clar ha h inrs is ing applid (compoundd) four ims a yar or quarrly. Thus, i maks sns o round o h nars quarr of a yar.. If h populaion of Ashmor, Illinois is dcrasing y.8% pr yar, hn y wha prcn will i dcras in h n yars? Show how you arrivd a your rsul. Round o h nars nh of a prcn. 00%.8% 9.% of h populaion rmains % of h populaion rmains afr yars 00% 7.%.8% populaion dcras

9 6. In financ, hr is a rul of hum ha is usd o sima h numr of yars i aks for an invsmn o doul in valu, known as Th Rul of 70. I sas ha if h coninuous compound prcn is known, hn h douling im, in yars, can simad y dividing 70 y ha prcn (wihou urning i ino a dcimal ra). If an invsmn is compoundd a a coninuous ra of %, hn how dos h rsul from h Rul of 70 compar o h ac amoun of im i aks o doul? Rul of 70 Esima 70 yars 70 yars Eac Tim: Us h coninuous compound formula 70 yars P.0.0 P.0 ln ln.0 ln ln.86 yars.0 A P r 7. A liquid wih an iniial mpraur of 9 F cools in a room whos mpraur is hld a 68 F. Th mpraur of h liquid, T, as i cools can modld as a funcion of im,, using: k T T T T i r r Whr T i is h iniial mpraur, T r is h mpraur of h room and k is h dcay consan. (a) If T 0 hn find h valu of k accura o h nars hundrdh. k T T k k k k 6 k ln ln 6 k ln 6 ln 6 k k () How many minus dos h modl prdic i will ak for h liquid o rach a mpraur of 70 F? Round o h nars minu and show or plain how you arrivd a your answr..09 T ln ln 6.09 ln 6 ln 6 6 min.09.09