k^x-x^k slider

This applet compares the values of [math]k^x[/math] and [math]x^k[/math]. When k=e, the graph is non-negative, and k=e is the only value for which [math]k^x≤x^k[/math] for all x. A nice activity for exploring exponents is to have students play a finger game where (like "Rock Paper Scissors") they each hold out 1 to 5 fingers. Their own number is the base, the other player's the exponent, highest score wins (e.g. if I hold 5 fingers and you 2, then you win because 5^2<2^5). Then extend and allow each person to write any positive number on a piece of paper. This applet is easy enough to make yourself -- I put it up as part of an article I'm writing about several related problems. I am new to GeoGebra Tube, and if there are two copies, it's because I'm trying to get it the right shape for embedding on my site.

 

dborkovitz

 
Resource Type
Activity
Tags
exponents 
Target Group (Age)
15 – 18
Language
English (United States)
 
 
GeoGebra version
4.0
Views
1759
Report a problem
 
 
© 2018 International GeoGebra Institute