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expanded on last paragraph; added internal link; minor correction
*(''x''<sup>0.5</sup>) · (''x''<sup>0.5</sup>) = ''x''<sup>1</sup> = ''x''
*(''x''<sup>0.5</sup>) · (''x''<sup>0.5</sup>) = ''x''<sup>1</sup> = ''x''
The sequence x<sup>1</sup>, x<sup>1</sup>, x<sup>2</sup>, x<sup>3</sup>, ... is an example of what can be called a [[geometrical progression]], [[compound interest]] growth, or [[exponential growth]]. These are all different names for the same thing. Because of the compounding effect, exponential growth occurs faster and faster... literally like wildfire. This has led to the colloquial use of the word ''exponential'' to mean "growing very rapidly," or even "very large."
The sequence x<sup>0</sup>, x<sup>1</sup>, x<sup>2</sup>, x<sup>3</sup>, ... is an example of what can be called a [[geometrical progression]], [[compound interest]] growth, or [[exponential growth]]. These are all different names for the same thing. Because of the compounding effect, exponential growth occurs faster and faster... literally like wildfire. This has led to the colloquial use of the word ''exponential'' to mean "growing very rapidly," or even "very large." The same sequence except with negative exponents would describe [[exponential decay]].
[[Category:Mathematics]]
[[Category:Mathematics]]