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15.) Complete the below table by determining the pattern. Then decide if the relationship is linear or exponential. Input Output 25 28 2. 31 3 4. 1.

15.) Complete the below table by determining the pattern. Then decide if the relationship is linear or exponential. Input Output 25 28 2. 31 3 4. 1.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Challenge 15: Identifying Patterns in a Table** You are given a table that requires completion based on an identifiable pattern. The aim is to decide whether the relationship between input and output is linear or exponential. **Table Data** | Input | Output | |-------|--------| | 0 | 25 | | 1 | 28 | | 2 | 31 | | 3 | | | 4 | | **Task:** 1. Analyze the given data in the table to determine the pattern. 2. Use the pattern to fill in the missing output values for inputs 3 and 4. 3. Decide if the relationship between input and output is linear (consistent rate of change) or exponential (consistent rate of multiplication). **Analysis:** - Observe the change between consecutive outputs: - From input 0 (Output: 25) to input 1 (Output: 28), the output increases by 3. - From input 1 (Output: 28) to input 2 (Output: 31), the output again increases by 3. This consistent increment of 3 suggests that the relationship might be linear, as the output appears to increase by the same amount for each unit increase in input. **Predicted Completion:** If the pattern continues: - For input 3: 31 + 3 = 34 - For input 4: 34 + 3 = 37 **Conclusion:** Based on the observed pattern of increasing by 3, the relationship is linear.
Transcribed Image Text:**Challenge 15: Identifying Patterns in a Table** You are given a table that requires completion based on an identifiable pattern. The aim is to decide whether the relationship between input and output is linear or exponential. **Table Data** | Input | Output | |-------|--------| | 0 | 25 | | 1 | 28 | | 2 | 31 | | 3 | | | 4 | | **Task:** 1. Analyze the given data in the table to determine the pattern. 2. Use the pattern to fill in the missing output values for inputs 3 and 4. 3. Decide if the relationship between input and output is linear (consistent rate of change) or exponential (consistent rate of multiplication). **Analysis:** - Observe the change between consecutive outputs: - From input 0 (Output: 25) to input 1 (Output: 28), the output increases by 3. - From input 1 (Output: 28) to input 2 (Output: 31), the output again increases by 3. This consistent increment of 3 suggests that the relationship might be linear, as the output appears to increase by the same amount for each unit increase in input. **Predicted Completion:** If the pattern continues: - For input 3: 31 + 3 = 34 - For input 4: 34 + 3 = 37 **Conclusion:** Based on the observed pattern of increasing by 3, the relationship is linear.
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