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.

Tree Structure

Properties of exponential trees

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 top-most level of the tree. The leaves can also be though of as the total population.

Math Operators

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.

Example 1

An exponential tree demonstrated 2 raised to 3.
Operation Relationship
Exponent
Logarithm
Radical

Example 2

An exponential tree demonstrated 3 raised to 2.
Operation Relationship
Exponent
Logarithm
Radical

Example 3

An exponential tree demonstrated 2 raised to 4.
Operation Relationship
Exponent
Logarithm
Radical