Iterations An Introduction Exit Animations Slide 17 1

Iterations An Introduction Exit Animations Slide 1/7 1. 1 Iterations: an Introduction

65536 256 1642 Iteration: A repetitive process wherein output from the prior stage becomes input for the next stage A repetitive numerical squaring process: 2 4 16 Exit 256 65536… Animations Slide 2/7 1. 1 Iterations: an Introduction

A repetitive geometric iteration process 6 5, 6 Select a random starting point Roll the die to identify a corner. Place the next point 1/2 way between the prior point and the selected corner 3 1 5 2 Repeat the prior step Thousands of Repetitions… 1, 2 Exit Animations 3, 4 Slide 3/7 1. 1 Iterations: an Introduction

Iteration on a Spreadsheet Problem Solvers can: =RANDBETWEEN(1, 6) Use built in spreadsheet functions designed to generate random numbers. Write formulas to produce values based upon those in prior cells. Exit Animations Slide 4/7 1. 1 Iterations: an Introduction

Spreadsheet Iteration applied to Monetary Growth Invest $1000 At 7% Compounded Monthly Year by Year Account Value Exit Animations Interest is repeatedly added based upon prior period value Slide 5/7 1. 1 Iterations: an Introduction

Many Natural Growth Processes Display Iterative Behaviors Repeatedly add a copy of the tree as it appeared prior to the last addition. Exit Animations Slide 6/7 1. 1 Iterations: an Introduction

Once represented numerically… …iterative processes can be explored by spreadsheets. ITERATIONS Excel Link an exploration of iterative processes. Exit Animations Slide 7/7 Word Link 1. 1 Iterations: an Introduction