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Graph of Exponentials

It's time to find out what these exponential things look like.

A few lessons ago, we found that the growth of a monster was described by

h( t ) = 2^( t )

Let's graph it!

To make it easier, let's graph

y = 2^( x ) ... since we're used to ( x , y ) guys

Well, when we have no idea what something looks like...  we have to plot points:

x: -2 , -1 , 0 , 1 , 2 ... y: 2^( -2 ) = ( 1 / 4 ) , 2^( -1 ) = ( 1 / 2 ) , 2^ ( 0 ) = 1 , 2^( 1 ) = 2 , 2^( 2 ) = 4a graph of y = 2^( x )

This is the basic shape of an exponential:

y = a^( x )wherea > 1

 

graph of exponential growth ... graphs hug asymptotes (they get closer and closer and never touch.) ... y = 0 is a horizontal asymptote. ... The bigger x gets, the faster it climbs

This is called "exponential growth."