Interactive Exponential Trees
This interactive demonstrates exponential growth using the structure of a tree. The tree has three important properties: the branching factor, the number of levels to the tree, and the number of leaves on the top level of the tree. These properties can be used to visualize the three math operators: exponent, logarithm, and radical operator.
The tree structure of this interactive has three important properties: the growth rate of the tree, the number of levels of the tree, and the number of leaves on the tree. These properties are highlighted in the figure above and summarized in the table below.
Variable  Property 

Growth Rate The growth rate, sometimes referred to as the base, describes the branching factor at each level of the tree. 

Levels The number of levels the tree where the starting point of the tree is considered level zero. The levels can also be thought of as time elapsed. 

Leaves The number of nodes on the topmost level of the tree. The leaves can also be though of as the total population. 
Each of the three operators: the exponent, logarithm and radical operator, corresponds to a property of the tree. Specifically, given two other properties as input, each operator returns the missing third property of the tree. Each relationship the operators have to the tree is summarized in the table below.
Equation  Operator 

Exponent Given the branching factor and the number of levels of the tree, the exponent operator returns the number of leaves on the tree. 

Logarithm Given the branching factor and leaves of the tree, the logarithm operator returns the levels of the tree. 

Radical Given the levels of the tree and the number of leaves, the radical operator returns the growth rate of the tree. 
Shown below are some examples of trees with unique properties that demonstrate these operator relationships.
Operation  Relationship 

Exponent  
Logarithm  
Radical 
Operation  Relationship 

Exponent  
Logarithm  
Radical 
Operation  Relationship 

Exponent  
Logarithm  
Radical 