Difference between revisions of "Exponential function"
| Line 15: | Line 15: | ||
Exponential functions are in one of three forms. | Exponential functions are in one of three forms. | ||
| − | :<math>f\left( x \right) = ab^x </math> | + | :<math>f\left( x \right) = ab^x </math>, where ''b'' is the % change written in decimals |
:<math>f\left( x \right) = ae^k </math>, where ''e'' is the irrational constant ''2.71828182846....'' | :<math>f\left( x \right) = ae^k </math>, where ''e'' is the irrational constant ''2.71828182846....'' | ||
:<math>f\left( x \right) = a\left( {{1 \over 2}} \right)^{{x \over h}} | :<math>f\left( x \right) = a\left( {{1 \over 2}} \right)^{{x \over h}} | ||
Revision as of 06:20, 10 November 2006
The exponential function is the function 
, exponentiation by e. It is a very important function in analysis, both real and complex.
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.
this page is still under construction...more to come very soon
