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Exponential and Logarithmic Functions
Barnett, Ziegler, and Byleen, chapter 5
I like to think of mathematics as a vast musical instrument on which
one can play a great variety of beautiful melodies.
Donald Knuth
sections:
5-1, 5-2, 5-3, 5-4
The exponential function and its inverse, the logarithm function have a number of uses in modeling real
phenomena. Up to this chapter, we have generally been solving problems exactly, expressing the results
as rational numbers with square roots of natural numbers where necessary. Now we will be evaluating
these functions with a calculator and approximating the solutions.
objectives:
- define ax where x is a real number
- calculate ax using a calculator
- use the laws of real exponents
- graph the exponential function ax
- tell how the graph changes for a>1 and a<1
- apply the exponential equation to problems of exponential growth and decay
- give an approximate value for e, the base of natural exponentials
- calculate ex using a calculator
- graph the natural exponential function
- tell how the graph of ekx changes with k
- apply the natural exponential function
- use the natural exponential function for compound interest
- define a logarithmic function
- give the relationship between an exponential function and a logarithmic function
- tell the values of the logarithms at 1 and a
- graph logarithmic functions
- give the domain of logarithmic functions
- use the laws of logarithms
- calculate common logarithms
- calculate natural logarithms
- apply logarithmic functions to physical problems
- express logarithms in one base to logarithms of another base
- calculate a logarithm function in any given base
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© 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008 by Lawrence Turner |