(a) Find all equilibria of N +1= 2.2N4, t= 0, 1, 2,. (b) Use cobwebbing to determine the stability of the equilibria found in (a). OA. OB. OD. AN.1 10- 10- 10- 10어 N. 10 3.5 10 10 3.5 Determine which equilibria are stable. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The stable equilibria are N= (Type an integer or a decimal. Use a comma to separate answers as needed.) O B. There are no stable equilibria.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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The problem requires determining which equilibria are stable for the equation \( N_{t+1} = 2.2N_t \) with \( t = 0, 1, 2, \ldots \). The instruction is to use cobwebbing to determine the stability of the equilibria found.

**Graphs Explanation:**

There are four graphs labeled A, B, C, and D. Each graph plots \( N_{t+1} \) against \( N_t \).

- The graphs show straight lines representing the function \( N_{t+1} = 2.2N_t \) and the identity line \( N_{t+1} = N_t \).
- Each graph contains a cobweb diagram starting from an initial point and iterates using vertical and horizontal moves to graphically represent successive values of \( N_t \).
- The x-axis is labeled \( N_t \) and ranges from 0 to 10.
- The y-axis is labeled \( N_{t+1} \) and ranges from 0 to 10.

**Task:**

Determine which equilibria are stable. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

- **Option A:** The stable equilibria are \( N = \) (Type an integer or a decimal. Use a comma to separate answers as needed.)
- **Option B:** There are no stable equilibria.
Transcribed Image Text:The problem requires determining which equilibria are stable for the equation \( N_{t+1} = 2.2N_t \) with \( t = 0, 1, 2, \ldots \). The instruction is to use cobwebbing to determine the stability of the equilibria found. **Graphs Explanation:** There are four graphs labeled A, B, C, and D. Each graph plots \( N_{t+1} \) against \( N_t \). - The graphs show straight lines representing the function \( N_{t+1} = 2.2N_t \) and the identity line \( N_{t+1} = N_t \). - Each graph contains a cobweb diagram starting from an initial point and iterates using vertical and horizontal moves to graphically represent successive values of \( N_t \). - The x-axis is labeled \( N_t \) and ranges from 0 to 10. - The y-axis is labeled \( N_{t+1} \) and ranges from 0 to 10. **Task:** Determine which equilibria are stable. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. - **Option A:** The stable equilibria are \( N = \) (Type an integer or a decimal. Use a comma to separate answers as needed.) - **Option B:** There are no stable equilibria.
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