Chapter 6.3, Problem 30E

To determine

To find: Four different patterns & model for each pattern.

Answer to Problem 30E

Four different patterns found& model for each pattern mentioned.

Explanation of Solution

Given information :

Given four different patterns.

Concept used:

Use patterns to determine type of function& model for each pattern.

Linear function: - The difference of consecutive y-values is constant.

Exponential function: - Consecutive y-values have a common ratio. In each case, the differences of consecutive x-values need to be constant.

  

1. Number of new branches = $y=2^{n-1}$ (Exponential function)
2. Length of new branches = $y={(\frac{1}{2})}^{n-1}$ (Exponential function)
3. Total length of all branches = $y=n$ (Linear function)
4. Total number of branches = $y=2^n-1$ (Exponential function)

Hence,

Four different patterns found & model for each pattern mentioned.