12.7

1
12.7 Fibonacci Sequence
2
I can recognize the Fibonacci Sequence

• 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,
• Whats 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