Difference between revisions of "Exponential function"

Revision as of 06:18, 10 November 2006

The exponential function is the function $f(x) = e^x$ , 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.

$f\left( x \right) = ab^x$

$f\left( x \right) = ae^k$ , where e is the irrational constant 2.71828182846....

$f\left( x \right) = a\left( {{1 \over 2}} \right)^{{x \over h}}$ or $f\left( x \right) = a\left( 2 \right)^{{x \over d}}$ , 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 $b > 1$ , then the funciton will show growth.

If $0 < b < 1$ , then the function will show decay.

this page is still under construction...more to come very soon

@@ Line 5: / Line 5: @@
 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'''''.
-Exponential functions are in one of three forms. <math>f\left( x \right) = ab^x </math>, <math>f\left( x \right) = ae^k </math>, where ''e'' is the irrational constant ''2.71828182846....'', or
-<math>f\left( x \right) = a\left( {{1 \over 2}} \right)^{{x \over h}}
+An exponential growth graph looks like:
-</math> <math>f\left( x \right) = a\left( 2 \right)^{{x \over d}}
+[[Image:2_power_x_growth.jpg]]
+An exponential decay graph looks like:
+[[Image:05_power_x_decay.jpg]]
+Exponential functions are in one of three forms.
+:<math>f\left( x \right) = ab^x </math>
+:<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> or <math>f\left( x \right) = a\left( 2 \right)^{{x \over d}}
 </math>, 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 <math>b > 1</math>, then the funciton will show growth.
+:If <math>0 < b < 1</math>, then the function will show decay.
 ''this page is still under construction...more to come very soon''

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Difference between revisions of "Exponential function"

Revision as of 06:18, 10 November 2006