Solve each equation Solve each equation. lne 38. Solve each equation.

Transcription

1 WS- Eponen/Log Review Day This should be done WITHOUT using your calculaor. Solve each equaion.. Simplify... n y y Change each equaion o logarihmic form Change each equaion o eponenial form.. log. log9. log. log0 0.0 Solve each equaion.. log. log log. log 7 Evaluae each epression. 9. log 0. log 0. log 9.. log 7 n WS- Eponen/Log Review Day This should be done WITHOUT using your calculaor. Solve each equaion. log log.. y 9 9. log log log log 0 0. log log 7 Use log and log o evaluae each epression. 7. log0. log0 9. log0 7 Solve each equaion. 0. log log.. log log log. log log log log log log Use he change of base formula o wrie in erms of common logs only.. log. log9. log 0. Evaluae each epression. 7. lne. Solve each equaion. 0. ln ln. log e e 9. ln0 e ln e. Graph he following on graph paper. Idenify each domain and range. G. y log G. y log G7. y log Graph he following on graph paper. G. y G. y G. y G. y

2 WS- Radioacive Decay and Logisics Day. The half-life of he radioacive krypon-9 is 0 seconds. If grams of he elemen are iniially presen, how many grams are presen 9 seconds?. The half-life of radioacive pluonium-9 is,000 years. If grams of he elemen are iniially presen, how many grams are presen afer 0,000 years?. Prehisoric cave painings were discovered in a cave in France. The pain conained % of he original carbon-. Esimae he age of he painings is he half-life for carbon- is 700 years.. Skeleons were found a a consrucion sie in San Francisco in 99. The skeleons conained % of he epeced amoun of carbon- found in a living person. How old were he skeleons in 99 if he half-life for carbon- is 700 years?. A bird species in danger of eincion has a populaion of 00 five years ago and oday only 000 of he birds are alive. Once he populaion drops below 00, he siuaion will be irreversible and eincion occurs. When will his happen?. The populaion of a single-celled organism in a pond doubles every days. If he iniial coun of organisms is 000 and he final coun is,000, how many days have passed? 7. A cerain srain of baceria increases from an iniial coun of 000 o a final coun of,000 in si hours. How long does i ake for his srain o riple?. A culure of baceria grew from 00 a :00pm o 000 a :00pm. Wha will he populaion be a 0:00pm? WS- Radioacive Decay and Logisics Day 9. During he firs week of flu season, 00 people became ill. Afer he h week, 00 had he flu, and afer he 7 h week, 00 were ill. a) Deermine he logisics model for his daa b) When will he flu oubreaks level off? 0. The percenage of -year olds wih some hear disease is 0.%, for 0-year olds wih some hear disease is % while he percenage of 0-year olds is 9%. a) Deermine he logisics model for his daa b) Wha percenage of 0-year olds have some coronary hear disease.. Shown is world populaion, in billions, for seven seleced years. Find he logisic regression o model his daa. According o he model, wha is he limiing size of he populaion ha he Earh will evenually susain? Wha does his mean in erms of he saemen made by he U.S. Naional Academy of Sciences ha 0 billion is he maimum ha he world can suppor wih some degree of comfor and individual choice?, Number of Years Afer 99 y, World Populaion (Billions) (90). (90).0 (970).7 (90). (990). (000). (00). Deermine he regression, eponenial or logisics, you would choose o model each daa se and why. Miscarriages in Women Women's Age Percen of Miscarriages Number of Counries Conneced o he Inerne Year # of Counries Number of Illegal Immigrans Living in he US # of US Households wih Pes Year # of Illegal # wih Pes Year Immigrans (Millions) (Millions) Alcohol Use by US High School Seniors Year % Usage 0 days Prior o Survey

3 WS- Compound Ineres Review. The value of a new car purchased for $,000 decreases by % each year. Esimae he value of he car afer wo years.. You deposi $000 in an accoun ha pays % annual ineres. Find he balance a he end of hree years if your ineres is compounded: a. Yearly? b. Quarerly? c. Monhly? d. Coninuously?. A newly married couple has $,000 oward a new home. How long will he money have o be invesed a 0% compounded quarerly o grow o he esimaed $0000 needed for a down paymen?. Sue has saved $7000 oward he purchase of a $9000 used car. How long will Sue's money need o be invesed a 9% compounded monhly unil she can buy he car?. Wha is he average rae of inflaion if a desk ha cos $0 in 990 cos $7 in 997? (Noe: Inflaion is compounded coninuously). The world populaion is approimaely.9 Billion people and growing a.% compounded coninuously. In wha year will he populaion reach 9 Billion people? WS- Effecive Annual Yield (Par of ) Find he effecive annual yield for each invesmen. Then find he value of a $000 invesmen afer years for each siuaion.. 0% compounded quarerly..% compounded monhly. 9.% compounded coninuously. 7.7% compounded coninuously..% compounded daily ( day year). Which invesmen yields more ineres 9% compounded coninuously or 9.% compounded quarerly? Go on o he ne column WS- Effecive Annual Yield (Par of ) Also complee he following (Taken from Page 7: - odd) Wrie he epression in eponenial form. Wrie he epression in logarihmic form.. log. Evaluae each epression.. log log log9 9. log Solve each equaion.. log0.. log log log Given ha log 0.77 and log., evaluae each logarihm. 9. log log0.0 WS- Fuure Value. A chemis deposis $00 in a savings accoun ha pays % ineres compounded annually and adds $00 a he end of each year for years. How much money does she have a he end of years?. Grandparens of a h grader decided o sar a college fund so ha in years heir grandchild will have $0,000 saved oward college uiion. Wha monhly paymens mus hey make if hey find a bank paying % ineres?. A -yr old man would like o have $00,000 in his accoun when he reires in 0 yrs. Wha monhly paymens should he make o an accoun ha pays % monhly?. A mah eacher deposis $000 in a savings accoun a he end of each quarer for 0 yrs. How much money does she have a he end of 0 yrs if he accoun pays.% compounded quarerly?. In yrs, a company wans o buy a new compuer sysem cosing $00,000. They esablish a sinking fund ha pays % compounded semiannually. To accumulae $00,000 in yrs, wha is he paymen every monhs?. A manufacurer deposis $000 each monh ino an accoun ha pays.% compounded monhly. He plans o do his for 7 years, how much money will be in he accoun a he end of ha ime period?

4 WS- Presen Value. Wha amoun of money mus be invesed oday a % compounded monhly so ha paymens of $00 per monh can be made from his fund for years?. A elevision is purchased for $00 down and $0 a monh for monhs. If he finance charge is % compounded monhly, find he original price of he se.. Wha are he monhly paymens o finance a $,000 car a % ineres for years? How much ineres was paid? Wha is he oal price of he car?. Wha is he highes priced price a person can afford if he is willing o pay monhly car paymens of $0 for he ne years wih he ineres rae a %?. You decide o purchase a house for $0,000. Your parens give you he 0% down paymen. Find he monhly house paymens if you are able o ge a 0-year loan a ½% compounded monhly. How much ineres was paid? Wha was he oal cos of he house?. In order for you no o work while in college, a fund is se up o pay you $00 a monh for years. How much should be deposied in he fund which is paying % compounded monhly o achieve his goal? How many monhs were you able o live off your ineres? WS- Review- Day. Radon has a half-life of. days. How long would i ake grams of decay o 0. grams?. How much should you deposi iniially in an accoun paying 0% compounded semi-annually in order o have $,000 in 0 years?. Which is he beer invesmen and why: 9% compounded quarerly or 9.% compounded annually?. A company esablishes a sinking fund o replace equipmen in years a an esimaed cos of $0,000. They plan o make monhly paymens ha pay % compounded monhly. How much should each paymen be?. If an accoun has $0,000, afer an iniial invesmen of $000, how long did i ake o accumulae his amoun a % wih simple ineres?. You can afford monhly deposis of $00 ino an accoun ha pays 7.9% compounded monhly. How long will i be unil you have $00 o purchase a used car? 7. A noon, a culure of baceria has. 0 members and a :00pm he culure had grown o. 0. When will he populaion be.0 0?. You decide o buy a house for $0,000 and are able o make a 0% down paymen. Wha is your monhly paymen if he loan is 7% compounded monhly for 0 years? How much did you pay in oal? How much ineres? WS- Review- Day 9. Wha is he ineres rae if $00 grew o $0,000 over years, compounded quarerly? 0. A ciy's populaion grew from 0,000 o 90,000 from How many people will here be in 0? In wha year will he populaion be,000,000?. The half-life of a subsance is 0 days. How much remains afer days?. An accoun has $0,000 afer an iniial invesmen of $000. How long was he accoun open if he money was compounded coninuously a %?. Wha is he inflaion rae if a car cos $,00 in 9 and now coss $,000?. A wha ineres rae would you need o have your money double in years compounded daily?. A scholarship commiee wishes o esablish a scholarship ha will pay $00 per quarer o a suden for wo years. How much should be deposied now, a % compounded quarerly, o esablish his scholarship? How much will he suden receive in wo years?. Find an eponenial funcion of he form y ab whose graph passes hrough he poins, and,

5 WS- Eponen/Log Review Day ANSWERS.. y. n. or. or. 7. log. log 9. log 9 0. log G. f() G.. f() WS- Eponen/Log Review Day ANSWERS.. y., log9 log G. f() G... log log. log0. log No Sol. ln. f() e G. f() G. - f() G7. - f()

6 WS- Radioacive Decay and Logisics Day ANSWERS y 0.0 y. grams , years r r 0.99 y years r, r hours y 0.0 y.7 grams years. 700, years.. r r.9 y baceria WS- Radioacive Decay and Logisics Day ANSWERS y 7. y 0.0 e e.7 y. Miscarriages in Women- 0.0 e Number of Illegal Immigrans- Households wih Pes- Inerne Connecion- Alcohol Use- ; Week -7 ; 7.90% WS- Compound Ineres Review ANSWERS. y, ; $ y 000 n a. Yearly? b. Quarerly? n 0.0 y 000 ; $ y 000 ; $ c. Monhly? y 000 ; $ d. Coninuously? y 000 e ; $ ,000,000 ;.9 years ;.0 years 7r 7 0 e ; r.% e ;. years from now WS- Effecive Annual Yield ANSWERS. E 0.0 ; 0.%; $.. E 0.0 ;.9%; $ E e ; 9.9%; $ E e ;.0%; $ ;.7%; $ a) E e ; 9.7%; $ b) ; 9.%; $7.

7 WS- Fuure Value ANSWERS Problem N= I%=.. PV= PMT= FV=.90 0,000 00, ,000 0,79.9 P/Y= C/Y= END/BEGIN END END END END END END WS- Presen Value ANSWERS Problem N= I%=. PV= PMT= FV= P/Y= C/Y= END/BEGIN END END END END END END. $. + $00 = $.. Toal: $.0 Ineres: $.0. Toal: $0.0 * 0 + $90000 = $.0 Ineres: $7.0. Ineres: $709. Time:.97 monhs

8 WS- Review- Day ANSWERS ;. years 0 0.0,000 P ; $ % EPY beer han 9.%. $7.. I pr..07 monhs 7. 0, ; Years r 0.. ; r..0.. ;.9 hours. $9.9; $,9.0 Toal; $,9.0 Ineres WS- Review- Day ANSWERS r 9. 0, ;.70% 0. 0 r 0 90,000 0,000 ; r.00 70,00 People in 0,000,000 in 0 (.7 years laer). y ; 0.% of original , e ; 7.9 years r,000,00 e ; r.7% in 0 r ;.%. $0,9.; $, b b y ;.9 y.9 or.9 Problem N= I%= PV= PMT= FV= P/Y= C/Y= END/BEGIN END END END END