5. Repeat the process for r = 4, but let x0 = 0.201. How does this behavior compare with the behavior for x0 = 0.2? 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?

Given values are Common Ratio, r=4 No. of terms, n=100 Initial value, x0=0.201 We compare other…

Answered: 5. Repeat the process for r = 4, but…

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5. Repeat the process for r = 4, but let x0 = 0.201. How does this behavior compare with the behavior for x0 = 0.2?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 64E

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

5. Repeat the process for r = 4, but let x₀ = 0.201. How does this behavior compare with the behavior for x₀ = 0.2?

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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