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Mortgages and Seashells

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1. Iterating Linear Functions

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A Useful Linear Function

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A General Financial Formula

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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

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-10000, B(n) = 0

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2. Iterating Geometric Transformations

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Rotate thru -90

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Dilate about the origin by a factor of.618

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Translate over 1, up 1

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Rotate thru -90

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Dilate about the origin by a factor of.618

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Translate over 1, up 1

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The Golden Spiral

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Golden Spiral?

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3. Iterating Complex Linear Functions

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3. Complex Linear Functions

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The Golden Rectangle Function

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Putting DeMoivres Theorem to Work

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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!