Difference between revisions of "Exponential function"
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| − | An exponential growth graph looks like:[[Image:2_power_x_growth.jpg]] | + | An exponential growth graph looks like: |
| + | [[Image:2_power_x_growth.jpg]] | ||
| − | An exponential decay graph looks like: [[Image:05_power_x_decay.jpg]] | + | An exponential decay graph looks like: |
| + | [[Image:05_power_x_decay.jpg]] | ||
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::<math>x = {{\ln \left( {{{56} \over {12}}} \right)} \over {\ln \left( {1.24976} \right)}}</math> | ::<math>x = {{\ln \left( {{{56} \over {12}}} \right)} \over {\ln \left( {1.24976} \right)}}</math> | ||
::<math>x \approx 6.9093</math> | ::<math>x \approx 6.9093</math> | ||
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Revision as of 09:32, 10 November 2006
The exponential function is the function 
, exponentiation by e. It is a very important function in analysis, both real and complex.
General Info and Definitions
Exponential functions are functions that grows or decays at a constant percent rate.
- Exponential functions that result in an increase of y is called an exponential growth.
- Exponential functions that result in an decrease of y is called an exponential decay.
An exponential growth graph looks like:
An exponential decay graph looks like:
Exponential functions are in one of three forms.
, where b is the % change written in decimals
, where e is the irrational constant 2.71828182846....
or 
, where h is the half-life (for decay), or d is the doubling time (for growth).
, where b is the % change written in decimals
, where e is the irrational constant 2.71828182846....
or 
, where h is the half-life (for decay), or d is the doubling time (for growth).
Whether an exponential function shows growth or decay depends upon the value of its b value.
- If
, then the funciton will show growth. - If
, then the function will show decay.
, then the funciton will show growth.
, then the function will show decay.
Solving Exponential Equations
There are two ways to solve an exponential equation. Graphically with a computer/calculator or algebraicly using logarithms.
Example: Solve 
- Graphically:
- Graph both equations and find the intersection.
- Algebraicly:
