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Chapter 4
Exponential and Logarithmic Functions
Section 4.1 introduces the
exponential function.
- An exponential function has a constant growth
factor.
Explain what this
means in your own words.
- How is an exponential function different from a linear
function?
- How can you calculate the value of the base of an exponential
function from a verbal description?
- What values are considered acceptable for use as
growth factors?
- How does the value of the growth factor affect the
increasing/decreasing
behavior of the graph?
- How can you calculate the growth
rate if you know the value of the growth factor?
- What is e?
- What does e have to do with exponential
functions?
- What is compound
interest? What is continuously
compounded interest?
Section 4.2 deals with
exponential models.
- What is doubling
time?
- What is half life?
- When would you use an exponential model
to solve a story problem?
Section 4.3 introduces the
logarithm function.
- Is the graph of the base 10 logarithm
function increasing or decreasing?
- How is a logarithmic function different
from an exponential function?
- How is a logarithmic function related
to an exponential function?
- How can you rewrite
an equation involving a log as an equation involving an exponential?
- How can e be used as a base for a log function?
- Why is it true that log
(1) = 0 ?
- Your calculator only calculates logs of base
10 or e.
How can you work with logs of other bases?
How does the base affect the graph, domain, range, asymptote, and properties
of the log function?
How can you use the inverse relationship
between logs and exponentials?
- There are three
very important properties of logarithmic functions. Summarize
these in the table below:
-
| |
What
is the property? |
Give
an example of how the property is used. |
| Mulitiplication
Property
|
|
|
| Power
Property
|
|
|
| Division
Property
|
|
|
Section 4.4 deals with
Logarithmic Models.
- What is the meaning of the word "magnitude"?
- Explain how the decibel scale works.
- Explain how the Richter scale works.
Section 4.5 introduces techniques for
solving exponential and log equations.
- How can you use a
logarithm to solve an equation involving an exponential?
- Be sure that you have memorized and know
how to use the 3 properties of logs:
Multiplication rule
Division rule
Power rule
- How are the three properties of logs used
to solve equations?
- How can you use the
inverse relationship between exponential and
log to solve equations?
- How can you use a
graph to solve an equation involving exponentials or logs?