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12.7 – Fibonacci Sequence

12.7 – Fibonacci Sequence. I can recognize the Fibonacci Sequence. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, … What’s the pattern?. Rabbits and Fibonacci. Each small rectangle will represent a pair of baby rabbits.

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12.7 – Fibonacci Sequence

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  1. 12.7 – Fibonacci Sequence

  2. I can recognize the Fibonacci Sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, … What’s the pattern?

  3. Rabbits and Fibonacci • Each small rectangle will represent a pair of baby rabbits. • It takes one month for a baby rabbit to mature and reproduce. (Represented by a big square tile) • Assume each mature rabbit reproduces one pair of baby rabbits every month and never die.

  4. 12.8 – Sequences & Iteration • I can iterate functions: • Iteration: composing a function with itself. • Iterate: the output of an iteration. • To iterate a sequence you will use the previous term to find the next term.

  5. Find the first four iterates of each function using the given initial value. • f(x) = 3x – 7; x0 = 4 5, 8, 17, 44 3(4) – 7 = 5 3(5) – 7 = 8 3(8) – 7 = 17 3(17) – 7 = 44

  6. Find the first four iterates of each function using the given initial value. Round to the nearest hundreth. 2. f(x) = 2x2 – x; x0 = 0.1 -0.08, 0.09, -0.07, 0.07 2(0.1)2 – 0.1 = -0.08 2(-0.08)2 – -0.08 = 0.09 2(0.09)2 – 0.09 = -0.07 2(-0.07)2 – -0.07 = 0.07

  7. Find the first three iterates of the function f(z) = 2z + (3-2i) for z0 = 1 + 2i 2(1 + 2i) + (3 – 2i) 2 + 4i + 3 – 2i 5 + 2i 2(5 + 2i) + (3 – 2i) 10 + 4i + 3 – 2i 13 + 2i 2(13 + 2i) + (3 – 2i) 26 + 4i + 3 – 2i 29 + 2i

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