Mortgages and Seashells. 1. Iterating Linear Functions.

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Presentation transcript:

Mortgages and Seashells

1. Iterating Linear Functions

A Useful Linear Function

A General Financial Formula

Suppose you borrowed $10,000 from a bank that charged.05% interest per month and would like to make payments of $500 per month. How long would it take to pay off the loan? An Application

-10000, B(n) = 0

2. Iterating Geometric Transformations

Rotate thru -90

Dilate about the origin by a factor of.618

Translate over 1, up 1

Rotate thru -90

Dilate about the origin by a factor of.618

Translate over 1, up 1

The Golden Spiral

Golden Spiral?

3. Iterating Complex Linear Functions

3. Complex Linear Functions

The Golden Rectangle Function

Putting DeMoivre’s Theorem to Work

Problem: This gives complex numbers as a function of a real variable. How do you plot g(x)? Need to plot ( real[g(x)], imaginary[g(x) ) for x = 0 to 20 Mathematica to the rescue!