# Mortgages and Seashells. 1. Iterating Linear Functions

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24-Dec-2015Category

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### Transcript of Mortgages and Seashells. 1. Iterating Linear Functions

- Slide 1
- Mortgages and Seashells
- Slide 2
- 1. Iterating Linear Functions
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- A Useful Linear Function
- Slide 7
- A General Financial Formula
- Slide 8
- 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
- Slide 9
- -10000, B(n) = 0
- Slide 10
- 2. Iterating Geometric Transformations
- Slide 11
- Rotate thru -90
- Slide 12
- Dilate about the origin by a factor of.618
- Slide 13
- Translate over 1, up 1
- Slide 14
- Rotate thru -90
- Slide 15
- Dilate about the origin by a factor of.618
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- Translate over 1, up 1
- Slide 17
- The Golden Spiral
- Slide 18
- Golden Spiral?
- Slide 19
- 3. Iterating Complex Linear Functions
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- Slide 21
- 3. Complex Linear Functions
- Slide 22
- The Golden Rectangle Function
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- Slide 24
- Putting DeMoivres Theorem to Work
- Slide 25
- 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!