COLLEGE ALGEBRA. Practice Problems Exponential and Logarithm Functions. Paul Dawkins
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1 COLLEGE ALGEBRA Practice Problems Eponential and Logarithm Functions Paul Dawkins
2 Table of Contents Preface... ii Eponential and Logarithm Functions... Introduction... Eponential Functions... Logarithm Functions... 4 Solving Eponential Equations... 5 Solving Logarithm Equations... 6 Applications Paul Dawkins i
3 Preface Here are a set of practice problems for my Algebra notes. If you are viewing the pdf version of this document (as opposed to viewing it on the web) this document contains only the problems themselves and no solutions are included in this document. Solutions can be found in a number of places on the site.. If you d like a pdf document containing the solutions go to the note page for the section you d like solutions for and select the download solutions link from there. Or,. Go to the download page for the site and select the section you d like solutions for and a link will be provided there.. If you d like to view the solutions on the web or solutions to an individual problem you can go to the problem set web page, select the problem you want the solution for. At this point I do not provide pdf versions of individual solutions, but for a particular problem you can select Printable View from the Solution Pane Options to get a printable version. Note that some sections will have more problems than others and some will have more or less of a variety of problems. Most sections should have a range of difficulty levels in the problems although this will vary from section to section. 007 Paul Dawkins ii
4 Eponential and Logarithm Functions Introduction Here are a set of practice problems for the Eponential and Logarithm Functions chapter of my Algebra notes. If you are viewing the pdf version of this document (as opposed to viewing it on the web) this document contains only the problems themselves and no solutions are included in this document. Solutions can be found in a number of places on the site. 4. If you d like a pdf document containing the solutions go to the note page for the section you d like solutions for and select the download solutions link from there. Or, 5. Go to the download page for the site and select the section you d like solutions for and a link will be provided there. 6. If you d like to view the solutions on the web or solutions to an individual problem you can go to the problem set web page, select the problem you want the solution for. At this point I do not provide pdf versions of individual solutions, but for a particular problem you can select Printable View from the Solution Pane Options to get a printable version. Note that some sections will have more problems than others and some will have more or less of a variety of problems. Most sections should have a range of difficulty levels in the problems although this will vary from section to section. Here is a list of topics in this chapter that have practice problems written for them. Eponential Functions Logarithm Functions Solving Eponential Equations Solving Logarithm Equations Applications Eponential Functions. Given the function f ( ) = 4 evaluate each of the following. (a) f ( ) (b) f ( ) (c) f ( 0) (d) f ( ) (e) f ( ). Given the function f ( ) = ( 5 ) evaluate each of the following. (a) f ( ) (b) f ( ) (c) f ( 0) (d) f ( ) (e) f ( ) 007 Paul Dawkins
5 . Sketch each of the following. (a) f ( ) = 6 (b) g( ) = 6 9 (c) g( ) 6 + = 4. Sketch the graph of ( ) f = e. = e Sketch the graph of ( ) f Logarithm Functions For problems write the epression in logarithmic form = =. = 9 For problems 4 6 write the epression in eponential form. 4. log = 5 5. log 5 65 = 4 6. log9 8 = For problems 7 - determine the eact value of each of the following without using a calculator. 7. log 8 8. log55 9. log 8 0. log ln e log Paul Dawkins 4
6 For problems 5 write each of the following in terms of simpler logarithms 4 7. log ( y ) 4. ln ( y ) + z log 4 y z For problems 6 8 combine each of the following into a single logarithm with a coefficient of one. log + 5log y log z ln ( t+ 5) 4ln t ln ( s ) 8. log a 6log b+ For problems 9 & 0 use the change of base formula and a calculator to find the value of each of the following. 9. log 5 0. log 5 For problems sketch each of the given functions.. g( ) = ln ( ). g( ) = ln ( + 5). g( ) ( ) = ln 4 Solving Eponential Equations Solve each of the following equations.. 6 = Paul Dawkins 5
7 = = = 7 5. = = 4 9 = 0 e e = 0 + = 0 Solving Logarithm Equations Solve each of the following equations.. log ( ) = log ( 5 ) 4 4. log ( 6) log ( 4 ) = log ( ). ln ( ) + ln ( + ) = ln ( 0 5) log 5 = 4. ( ) 5. ( ) ( ) log + log = 6. ( ) ( ) log + log 6 = log ( ) = log ( ) 8. ln ( ) = + ln ( + ) 9. ( ) ( ) log log 7 = Paul Dawkins 6
8 Applications. We have $0,000 to invest for 44 months. How much money will we have if we put the money into an account that has an annual interest rate of 5.5% and interest is compounded (a) quarterly (b) monthly (c) continuously. We are starting with $5000 and we re going to put it into an account that earns an annual interest rate of %. How long should we leave the money in the account in order to double our money if interest is compounded (a) quarterly (b) monthly (c) continuously. A population of bacteria initially has 50 present and in 5 days there will be 600 bacteria present. (a) Determine the eponential growth equation for this population. (b) How long will it take for the population to grow from its initial population of 50 to a population of 000? 4. We initially have 00 grams of a radioactive element and in 50 years there will be 80 grams left. (a) Determine the eponential decay equation for this element. (b) How long will it take for half of the element to decay? (c) How long will it take until there is only gram of the element left? 007 Paul Dawkins 7
CALCULUS I. Practice Problems. Paul Dawkins
CALCULUS I Practice Problems Paul Dawkins Table of Contents Preface... iii Outline... iii Review... Introduction... Review : Functions... Review : Inverse Functions... 6 Review : Trig Functions... 6 Review
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