Advanced Algebra
Unit 4: Exponential and
Logarithms
Excerpts from Georgia
Department of Education
Webinar October 3, 2013
melissa.stewart@hallco.org
October 2013
Warm-Up
Four physicists describe the amount of radioactive substance,
in grams, left after
years.
Are the four equations equivalent?
Solution:
Are the four equations equivalent? YES
melissa.stewart@hallco.org
October 2013
What’s the main idea of Unit 4?
•
•
•
•
Write expressions in equivalent forms to solve problems
Analyze functions using different representations
Build new functions from existing functions
Construct and compare linear, quadratic, and exponential models and solve
problems.
Concepts & Skills to Maintain from Previous Grades

 The concept of a function
 Various representations of functions
 Exponential functions and characteristics of their graphs
The solution of linear equations using algebra and graphing approaches
 Familiarity with graphing technology
 Use patterns to write a function to model a situation
Websites to help with the above:
http://www.crctlessons.com/
www.aplusmath.com
www.aaamath.com
Enduring Understandings from this Unit


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There is an inverse relationship between exponents and logarithms.
Logarithms can be used to solve exponential equations.
An exponential equation can be written as a logarithmic equation; a logarithmic equation
can be written as an exponential equation.
Two special logarithmic functions are the common logarithmic function and the
natural logarithmic function. These special functions occur often in nature.
Common logarithms and natural logarithms can be used to evaluate logarithms with
bases other than 10 or .
melissa.stewart@hallco.org
October 2013
Examples & Explanations
Problem 1:
A hospital is conducting a study to see how different environmental conditions influence the
growth of streptococcus pneumonia. Explain in terms of the structure of the expressions defining
and
, why these two populations never share the same value at any time
during the experiment.
Solution:
and grows at a rate based on
and grows at a rate based on
Since
and
,
>
melissa.stewart@hallco.org
October 2013
Problem 2: By definition
yield
(
is the exponent which must be raised in order to
).
Use this definition to compute:
Solution:
melissa.stewart@hallco.org
October 2013
Problem 3: Graphene is a 1 atom thick layer of graphite with many interesting properties and
uses. Suppose the thickness of graphene is 200 picometers: one picometer is one trillionth of a
meter. About how many times would you have to split a 1 mm thick sample of graphite in half in
order to get a single layer of graphene?
Solution:
picometers in one millimeter.
Cutting in half
times yield a thickness of
millimeters or
picometers.
Problem 4: What is the relationship between the graphs of exponential functions and logarithmic
functions?
Solution: By analyzing the graph, they are inverses.
melissa.stewart@hallco.org
October 2013

The student edition for Unit 4 can be found at
https://www.georgiastandards.org/Common-Core/Pages/Math-9-12.aspx On the left
side, please look under mathematics, Accelerated Geometry B/Advanced Algebra.
Then, the right side has a pull-down menu to access the units.

Additional parent guides will be posted to the parent resource page on
http://www.hallco.org/boe/index.php (right hand menu) as they become available.
melissa.stewart@hallco.org
October 2013