UNIT #4 TEST REVIEW EXPONENTIAL AND LOGARITHMIC FUNCTIONS

Transcription

1 Name: Par I Quesions UNIT #4 TEST REVIEW EXPONENTIAL AND LOGARITHMIC FUNCTIONS Dae: 1. The epression 1 is equivalen o 1 () () 6. The eponenial funcion y 16 could e rewrien as y () y 4 () y y. The epression a is equivalen o which of he following as long as a 0? a () a () a a 4. Which of he following would give he same resul as 4? 8 () () For he funcion 7 () 1 () 17 f 7, which of he following represens is y-inercep?

2 6. Which of he following could e he equaion of he graph shown elow? y 100. () y 0.7 () y 41. y. y a 7. Seleced values of an eponenial funcion of he form which of he following represens he value of? are shown elow. To he neares hundredh, 1.1 () 1.78 () y ? 8. Which of he following values of solves: 4 () 9 () 7 9. In erms of he unknown consan a, which of he following values of solves: 7 a () 8 a a 1 9 a? () 4 a 4a 10. A populaion of frui flies is increasing a a rae of.% per hour. If he populaion had an original size of 10 flies, hen which of he following is is size afer one day? 798 () 11 () 9 104

3 11. The waer level in a draining reservoir is changing such ha he deph of waer decreases y 7.% per hour. If he waer sars a a deph of 4 fee, hen which of he following funcions properly models he deph, d, as a funcion of ime,, in hours since i sared draining? d 4.07 () d 47. () d 4.9 d The emperaure of a cooling liquid in a room held a a consan 7 degrees Fahrenhei can e descried y he equaion F , where F is he Fahrenhei emperaure and is he amoun of ime i has een cooling, in minues. Which of he following was he original emperaure of he liquid when i egan cooling? 7 () 0 () If a populaion grows a a consan rae of.8% per year, hen y wha percen will i grow over he ne 10 years? 17% () % () 8% 9% 14. The half-life of a radioacive maerial is he amoun of ime i akes for 0% of is radioaciviy o decrease. If a paricular maerial has a half-life of years, hen wha percen will remain radioacive afer 100 years? 1.8% () 4.8% ().7% 48.7% 1. Which of he following is closes o he value of log 4 40? 1.8 ().7 ()..

4 16. If 0 hen 1 () 1 log is equal o () 17. Given he funcion f log 8 funcion?, which of he following values of is no in he domain of he () 8 () Which of he following equaions is shown graphed on he grid elow? y () y 4 () ylog ylog Which of he following is equivalen o log y? log log y () log log y () log log y 4log log y 0. If log 1. hen log 1? 0.4 ().6 ()

5 1. If 7 hen log 7 () log 1.4 () 7 7. If f hen which of he following values of solves he equaion 1.1 () 1.8 () f 90? k. If ae c 0 hen which of he following is he value of ased on a, k, and c and he naural ase e? 1 ln c k a c () ln ak () ln c ak ac ke 4. If $00 is placed in a savings accoun ha earns a 6% nominal ineres compounded monhly, hen which of he following represens he accoun s worh afer 10 years? $ () $89.4 () $87.9 $ How many years, o he neares enh, would i ake for an invesmen o doule if i is earning a coninuous compound ineres of.% per year? 17.4 years (). years () 19.8 years.1 years

6 k 6. If a liquid is cooling down according o he formula y84e and a hen which of he following is he value of k o he neares hundredh? he emperaure is y 71 () 0.08 () The emperaure of a cooling liquid is given y he funcion m T m , where T represens he emperaure in degrees Celsius and m represens he numer of minues,, ha he liquid has een cooling. Which of he following represens a emperaure ha he liquid does no reach as i cools down? () 41 () 16 8 m 0 Free Response Quesions 8. On he grid shown elow, he graph of f is shown. (a) On he same graph grid, creae an accurae skech of 1 his funcion s inverse, f. () Sae he equaion of f 1. (c) Sae he domain and range of oh 1 f and f. 1 f f Domain: Range: Domain: Range:

7 9. An ojec is slowing down such ha is speed is decreasing eponenially. If afer seconds i is raveling a 8 fee per second and afer seconds i is raveling a only 11 fee per second, hen find an equaion in he form y a for he speed, y, as a funcion of he numer of seconds,, ha have passed. Find he equaion using algeraic echniques. Round oh a and o he neares hundredh. 1 can e wrien as a in simples form. Deermine he value of a. Show how you arrived a your answer. 0. The epression 1. If g 1 7 hen algeraically deermine he soluion o he equaion g.. For he logarihmic funcion f log 4, eplain why 0 is no in is domain.

8 . For some ase,, i is known ha of. Eplain how you found your answer. log 40 log 1.8 and log 0.. For he same ase, deermine he value.0 801, where w represens he 4 worh in dollars and represens he numer of years since he principal was deposied ino he accoun. Algeraically deermine he numer of years, o he neares quarer of a year, i akes for he accoun o e worh $ A ank accoun s worh can e modeled using he formula w 4 Why does i make sense o round your answer o he neares quarer of a year?. If he populaion of Ashmore, Illinois is decreasing y.8% per year, hen y wha percen will i decrease in he ne years? Show how you arrived a your resul. Round o he neares enh of a percen.

9 6. In finance, here is a rule of hum ha is used o esimae he numer of years i akes for an invesmen o doule in value, known as The Rule of 70. I saes ha if he coninuous compound percen is known, hen he douling ime, in years, can e esimaed y dividing 70 y ha percen (wihou urning i ino a decimal rae). If an invesmen is compounded a a coninuous rae of %, hen how does he resul from he Rule of 70 compare o he eac amoun of ime i akes o doule? Rule of 70 Esimae Eac Time: Use he coninuous compound formula A Pe r 7. A liquid wih an iniial emperaure of 194 o F cools in a room whose emperaure is held a 68 o F. The emperaure of he liquid, T, as i cools can e modeled as a funcion of ime,, using: k T T T e T i r r Where T i is he iniial emperaure, T r is he emperaure of he room and k is he decay consan. (a) If T 1 10 hen find he value of k accurae o he neares hundredh. () How many minues does he model predic i will ake for he liquid o reach a emperaure of 70 F o? Round o he neares minue and show or eplain how you arrived a your answer.