3. For r = 3.2 and r = 3.5, calculate the first 100 sequence values. Generate a cobweb diagram for each iterative process. (Several free applets are available online that generate cobweb diagrams for the logistic map.) What is the long-term behavior in each of these cases? f(x)3.55x(1x)Figure 2 A cobweb diagram for f(x) = 3.55x(1 – x) is presented here. The sequence of values results in an 8 -cycle.1. Let r = 0.5 and choose xo = 0.2. Either by hand or by using a computer, calculate the first 10 values in thesequence. Does the sequence appear to converge? If so, to what value? Does it result in a cycle? If so, whatkind of cycle (for example, 2 - cycle, 4 -- cycle.)?2. What happens when r = 2?3. For r = 3.2 and r =3.5, calculate the first 100 sequence values. Generate a cobweb diagram for eachiterative process. (Several free applets are available online that generate cobweb diagrams for the logisticmap.) What is the long-term behavior in each of these cases?4. Now let r = 4. Calculate the first 100 sequence values and generate a cobweb diagram. What is thelongterm behavior in this case?5. Repeat the process for r = 4, but let xo = 0.201. How does this behavior compare with the behavior for xo =0.2?

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Description: 3. For r = 3.2 and r = 3.5, calculate the first 100 sequence values. Generate a cobweb diagram for each iterative process. (Several free applets are available online that generate cobweb diagrams for the logistic map.) What is the long-term behavior

Given values are The two common ratios are r1=3.2 and r2=3.5 No. of terms, n=100 The initial value,…

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3. For r = 3.2 and r = 3.5, calculate the first 100 sequence values. Generate a cobweb diagram for each iterative process. (Several free applets are available online that generate cobweb diagrams for the logistic map.) What is the long-term behavior in each of these cases?

3. For r = 3.2 and r = 3.5, calculate the first 100 sequence values. Generate a cobweb diagram for each iterative process. (Several free applets are available online that generate cobweb diagrams for the logistic map.) What is the long-term behavior in each of these cases?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.5: Properties Of Logarithms

Problem 42E

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Concept explainers

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Question

f(x)
3.55x(1
x)
Figure 2 A cobweb diagram for f(x) = 3.55x(1 – x) is presented here. The sequence of values results in an 8 -
cycle.
1. Let r = 0.5 and choose xo = 0.2. Either by hand or by using a computer, calculate the first 10 values in the
sequence. Does the sequence appear to converge? If so, to what value? Does it result in a cycle? If so, what
kind of cycle (for example, 2 - cycle, 4 -
- cycle.)?
2. What happens when r = 2?
3. For r = 3.2 and r =
3.5, calculate the first 100 sequence values. Generate a cobweb diagram for each
iterative process. (Several free applets are available online that generate cobweb diagrams for the logistic
map.) What is the long-term behavior in each of these cases?
4. Now let r = 4. Calculate the first 100 sequence values and generate a cobweb diagram. What is the
longterm behavior in this case?
5. Repeat the process for r = 4, but let xo = 0.201. How does this behavior compare with the behavior for xo =
0.2?

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