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For the discrete logistic equation xt + 1 = Cxt(1 – Xt) and the given values of xo and c, calculate Xt to four decimal places for t = 1, 2, ..., 10. Xo = 0.6, c = 1.5 t Xt 0.6000 1 0.384 3 4 5 6 8 9 10 Graph Xt. 0.6 xt 0.7 xt 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2

For the discrete logistic equation xt + 1 = Cxt(1 – Xt) and the given values of xo and c, calculate Xt to four decimal places for t = 1, 2, ..., 10. Xo = 0.6, c = 1.5 t Xt 0.6000 1 0.384 3 4 5 6 8 9 10 Graph Xt. 0.6 xt 0.7 xt 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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For the discrete logistic equation \( x_{t+1} = c x_t (1 - x_t) \) and the given values of \( x_0 \) and \( c \), calculate \( x_t \) to four decimal places for \( t = 1, 2, \ldots, 10 \). Given: - \( x_0 = 0.6 \) - \( c = 1.5 \) | \( t \) | \( x_t \) | |---------|------------| | 0 | 0.6000 | | 1 | 0.384 | | 2 | | | 3 | | | 4 | | | 5 | | | 6 | | | 7 | | | 8 | | | 9 | | | 10 | | Graph \( x_t \): The graph shows a series of blue dots representing the values of \( x_t \) over time \( t \). The x-axis represents \( t \), and the y-axis represents \( x_t \). The initial value at \( t = 0 \) starts at \( 0.6 \), then quickly stabilizes around \( 0.3 \) for the subsequent values of \( t \).
Transcribed Image Text:For the discrete logistic equation \( x_{t+1} = c x_t (1 - x_t) \) and the given values of \( x_0 \) and \( c \), calculate \( x_t \) to four decimal places for \( t = 1, 2, \ldots, 10 \). Given: - \( x_0 = 0.6 \) - \( c = 1.5 \) | \( t \) | \( x_t \) | |---------|------------| | 0 | 0.6000 | | 1 | 0.384 | | 2 | | | 3 | | | 4 | | | 5 | | | 6 | | | 7 | | | 8 | | | 9 | | | 10 | | Graph \( x_t \): The graph shows a series of blue dots representing the values of \( x_t \) over time \( t \). The x-axis represents \( t \), and the y-axis represents \( x_t \). The initial value at \( t = 0 \) starts at \( 0.6 \), then quickly stabilizes around \( 0.3 \) for the subsequent values of \( t \).
## Transcription and Diagram Explanation ### Diagrams The image contains two graphs side by side, each plotting a sequence over a given range of values. #### Left Graph - **Axes:** The vertical axis is labeled \( x_t \) and ranges from 0 to 0.8, while the horizontal axis is labeled \( n \) and ranges from 0 to 10. - **Plot:** The graph displays a series of blue dots representing the sequence values at different \( n \). The sequence starts at 0.8 and appears to decrease slightly, as subsequent points hover around 0.6. #### Right Graph - **Axes:** Similarly, the vertical axis is labeled \( x_t \), ranging from 0 to 0.8, and the horizontal axis is also labeled \( n \), ranging from 0 to 10. - **Plot:** A series of blue dots are plotted, with the sequence starting at 0.2 and slightly increasing as \( n \) progresses, stabilizing between 0.4 and 0.6. ### Questionnaire **Comment on the behavior of the sequence.** - ○ The sequence increases converging toward 1/3. - ○ The sequence decreases converging toward 1/2. - ○ The sequence increases converging toward 1/2. - ○ The sequence decreases converging toward 1/3. The graphs illustrate the behavior of two sequences over time. The left graph depicts a sequence that slightly decreases, while the right graph shows a sequence that gradually increases. Based on these observations, one can analyze the convergence behavior and determine the most appropriate response from the options provided.
Transcribed Image Text:## Transcription and Diagram Explanation ### Diagrams The image contains two graphs side by side, each plotting a sequence over a given range of values. #### Left Graph - **Axes:** The vertical axis is labeled \( x_t \) and ranges from 0 to 0.8, while the horizontal axis is labeled \( n \) and ranges from 0 to 10. - **Plot:** The graph displays a series of blue dots representing the sequence values at different \( n \). The sequence starts at 0.8 and appears to decrease slightly, as subsequent points hover around 0.6. #### Right Graph - **Axes:** Similarly, the vertical axis is labeled \( x_t \), ranging from 0 to 0.8, and the horizontal axis is also labeled \( n \), ranging from 0 to 10. - **Plot:** A series of blue dots are plotted, with the sequence starting at 0.2 and slightly increasing as \( n \) progresses, stabilizing between 0.4 and 0.6. ### Questionnaire **Comment on the behavior of the sequence.** - ○ The sequence increases converging toward 1/3. - ○ The sequence decreases converging toward 1/2. - ○ The sequence increases converging toward 1/2. - ○ The sequence decreases converging toward 1/3. The graphs illustrate the behavior of two sequences over time. The left graph depicts a sequence that slightly decreases, while the right graph shows a sequence that gradually increases. Based on these observations, one can analyze the convergence behavior and determine the most appropriate response from the options provided.
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