COLLEGE ALGEBRA
These brief notes are intended to guide you through the textbook and/or other course readings/materials. As you read the textbook pay particular attention to the "topics of importance" and be sure you know how to accomplish each. The "supplemental sites" may provide additional resources on the internet that supplement the topics. Note: this material is extensively elaborated upon in my optional e-book GOLDen Mathematics: College Algebra. This section of material only is downloadable for a nominal fee at www.lulu.com/content/470022. See "Tell me more about Keely's GM book".
Exponential and Logarithmic Functions and Graphs
GOLDen Mathematics - College Algebra: Section 4.1
Supplemental Sites:
MathOL Links - Calg
4.1
Topics of Importance
Exponential function: definition, terminology, evaluate
Graphs of exponential functions: basic shape, domain, range, intercepts,
asymptotes, reflections, and shifts
e: definition, evaluate on calc
Logarithmic function: definition, common logarithm, natural logarithm
Graphs of logarithmic functions: basic shape, domain, range, intercepts,
asymptotes
Evaluate logarithms (by hand and on calc), change of base theorem
Convert logarithmic
exponential form
Properties of logarithms: basic properties & product, quotient, power rules
Simplify logarithmic expressions
Comments and Cautions
Much of the material in this lesson is review from an intermediate algebra
course. Our focus here though will be to expand on the basic
topics, bump up the level of difficulty, and get exponential and logarithmic
functions down really well :) As you work through the material, try to do what
you can algebraically as well as take advantage of technology where appropriate.
Be sure to watch the "Dr. Albert Bartlett: Arithmetic, Population and Energy" video linked from the supplemental sites. Highly recommended! There are also some fun sites worth checking out linked from "Liberal Arts Math Links - Growth and Scale" on the supplemental sites page.
Text Notes (These notes refer to College Algebra 4th ed by Blitzer section 4.1-4.3.)
 | ch 4.1 is pretty straight forward and mostly review from intermediate algebra. Be sure to be able to work problems both by hand and electronically. |
| ch 4.2 pg 421 Read "The Curious Number e" -- cool stuff! Want to learn more? Check out e - The Story of a Number by Eli Maor. Great school break reading! |
| ch 4.3 The change of base theorem can convert a log-base-b to a ratio of logarithms. Of all its possible forms the most useful is when it convert to a ratio of natural logarithms as in logbx = ln(x)/ln(b). Although logbx can be rewritten by the change of base theorem as a quotient of logarithms with any particular base, for instance logbx = log(x)/log(b), it is best in calculus to convert to a quotient of natural logs unless there is a specific reason to chose a different base. |
Exponential and Logarithmic Equations and Applications
GOLDen Mathematics - College Algebra: Section 4.2
Supplemental Sites:
MathOL Links - Calg 4.2
Topics of Importance
Solve logarithmic equations algebraically
Solve exponential equations algebraically
Solve exponential and logarithmic equations graphically
Applications of exponential and logarithmic functions including growth and decay
Comments and Cautions
Again, much of the material in this lesson is review from an intermediate
algebra course, particularly solving basic exponential or logarithmic equations.
Our focus will be to expand on the basic processes, bump up the level of
difficulty, and tackle some interesting and challenging equations that integrate
several methods of simplifying and solving (e.g. using the properties of
logarithms or converting between logarithmic and exponential forms).
May your knowledge of these functions grow exponentially ;-)
The growth and decay application problems include problems such as viruses spreading exponentially, nuclear waste decaying exponentially, and logarithmic learning curves. These will be important processes in calculus where our primary focus will be on the rate of change of this growth or decay.
Text Notes (These notes refer to College Algebra 4th ed by Blitzer section 4.4-4.5.)
| ch 4.4 Be sure that you can solve the problem both algebraically and graphically where appropriate. |
| ch 4.5 You are expected to memorize the exponential growth model formula (page 447). But the other formulas like Newton's Law of Cooling and the Logistic Growth Model you are not expected to memorize, but you should know how to use them if they were supplied as part of an application problem on an exam. |
Originally written: 2006-09-04
Last revision:
2008-06-02 01:13 AM