Chaos Theory Portfolio Algebra 2

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Anarchy Theory Portfolio
Directions: In this portfolio, you will use repeated part composition to explore elementary ideas that are used in the
mathematical field of chaos theory. Items under the Questions headings will be submitted to your teacher as office of
your portfolio assessment. For all questions, make sure to be consummate in your responses. This tin include details such
as the office being iterated, the initial values used, and the number of iterations. The phrase many iterations is used
in some of the questions. Translate that to mean using enough iterations so that you can come to a conclusion. If
necessary, round decimals to the nearest ten-thousandth.

Questions

1. If you continue this pattern, what do you look would happen to the numbers as the
number of iterations grows? Check your consequence past conducting at to the lowest degree 10 iterations.

2. Repeat the process with an initial value of -i. What happens as the number of iterations
grows?

Example two

Questions

3. What happens to the value of the role as the number of iterations increases?

4. Cull an initial value that is less than zero. What happens to the value of the role as
the number of iterations increases?

five. Come upwards with a new linear function that has a slope that falls in the range -1 < grand < 0.
Choose ii dissimilar initial values. For this new linear role, what happens to the
function'due south values afterward many iterations?

Are the function's values getting close to a particular number in each case?

6. Utilise the function g(ten) = -x + ii with initial values of 4, 2, and 1. What happens after many
iterations with all iii initial values?

How do the results of all three iterations relate to each other?

Questions

vii. What is the loop that forms later many iterations when the initial value of g is i.7?

8. What is the loop that forms after many iterations when the initial value of g is 1.72?

Questions
9. Cull an initial value that is between null and 4 and is not a whole number. Iterate it
using the function, f, ten times. If necessary, you can round your res...

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Chaos Theory Portfolio Algebra 2,

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