Difference between revisions of "Exponential function"
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The '''exponential function''' is the [[function]] <math>f(x) = e^x</math>, [[exponentiation]] by ''[[e]]''. It is a very important function in [[analysis]], both [[real]] and [[complex]]. | The '''exponential function''' is the [[function]] <math>f(x) = e^x</math>, [[exponentiation]] by ''[[e]]''. It is a very important function in [[analysis]], both [[real]] and [[complex]]. | ||
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| − | 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'''''. | + | == General Info and Definitions == |
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| + | 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'''''. | ||
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[[Image:2_power_x_growth.jpg]] | [[Image:2_power_x_growth.jpg]] | ||
| − | An exponential decay graph looks like: | + | An exponential decay graph looks like: [[Image:05_power_x_decay.jpg]] |
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| − | [[Image:05_power_x_decay.jpg]] | ||
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:If <math>b > 1</math>, then the funciton will show growth. | :If <math>b > 1</math>, then the funciton will show growth. | ||
:If <math>0 < b < 1</math>, then the function will show decay. | :If <math>0 < b < 1</math>, then the function will show decay. | ||
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| + | == Solving Exponential Equations == | ||
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| + | There are two ways to solve an exponential equation. Graphically with a computer/calculator or algebraicly using logarithms. | ||
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| + | '''Example:''' Solve <math>56 = 12\left( {1.24976} \right)^x </math> | ||
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| + | '''Graphically:''' | ||
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| + | Graph both equations and find the intersection. | ||
| + | [[Image:expfunc_graphsolve_eqn.jpg]] | ||
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| + | '''Algebraicly:''' | ||
Revision as of 09:22, 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:
this page is still under construction...more to come very soon
