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(i) For what x-values is 300(1.1)* > 200(1.2)*? 300(1.1)* > 200(1.2)* when x Sv i (ii) For what x-values is 300(1.1)* < 200(1.2)*? 300(1.1)* <200(1.2)* when x > V eTextbook and Media Hint

(i) For what x-values is 300(1.1)* > 200(1.2)*? 300(1.1)* > 200(1.2)* when x Sv i (ii) For what x-values is 300(1.1)* < 200(1.2)*? 300(1.1)* <200(1.2)* when x > V eTextbook and Media Hint

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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I chose the correct graph just solve the rest

### Educational Content: Understanding Exponential Functions through Graph Analysis #### Problem Question: Select the correct graph of \( y = 300(1.1)^x \) in blue and \( y = 200(1.2)^x \) in black using the points \( x = 1, 2, 3, 4, 5 \). #### Graph Analysis: The image contains two graphs which are described below: 1. **Graph 1 (Top Graph):** - **Axes:** The horizontal axis represents the variable \( x \) ranging from 1 to 5. The vertical axis represents the value of \( y \). - **Curves:** - **Blue Curve:** This graph depicts the equation \( y = 300(1.1)^x \). The curve starts at a moderate level and shows a gradual upward trend as \( x \) increases. This reflects a steady but slower exponential growth due to the base (1.1) being just above 1. - **Black Curve:** This graph represents the equation \( y = 200(1.2)^x \). The curve starts lower due to the initial value being 200 but shows a steeper upward trend compared to the blue curve. This indicates a faster exponential increase because the base (1.2) is larger. 2. **Graph 2 (Bottom Graph):** - Features are similar to the top graph, with noticeable growth trends in two exponential curves. - The same color-coding and axis labels are maintained. ### Conclusion: The exercise requires students to observe and interpret the characteristics of exponential functions, particularly the impact of different bases on the growth rate, by selecting the graph that correctly matches the given functions. This teaches how initial values and base multipliers affect the growth and how to visually analyze and differentiate between exponential graphs.
Transcribed Image Text:### Educational Content: Understanding Exponential Functions through Graph Analysis #### Problem Question: Select the correct graph of \( y = 300(1.1)^x \) in blue and \( y = 200(1.2)^x \) in black using the points \( x = 1, 2, 3, 4, 5 \). #### Graph Analysis: The image contains two graphs which are described below: 1. **Graph 1 (Top Graph):** - **Axes:** The horizontal axis represents the variable \( x \) ranging from 1 to 5. The vertical axis represents the value of \( y \). - **Curves:** - **Blue Curve:** This graph depicts the equation \( y = 300(1.1)^x \). The curve starts at a moderate level and shows a gradual upward trend as \( x \) increases. This reflects a steady but slower exponential growth due to the base (1.1) being just above 1. - **Black Curve:** This graph represents the equation \( y = 200(1.2)^x \). The curve starts lower due to the initial value being 200 but shows a steeper upward trend compared to the blue curve. This indicates a faster exponential increase because the base (1.2) is larger. 2. **Graph 2 (Bottom Graph):** - Features are similar to the top graph, with noticeable growth trends in two exponential curves. - The same color-coding and axis labels are maintained. ### Conclusion: The exercise requires students to observe and interpret the characteristics of exponential functions, particularly the impact of different bases on the growth rate, by selecting the graph that correctly matches the given functions. This teaches how initial values and base multipliers affect the growth and how to visually analyze and differentiate between exponential graphs.
Using the points in the graph from part (a), determine the following. Enter only integer values corresponding to the points from part (a) in the answer fields. (i) For what x-values is \(300(1.1)^x > 200(1.2)^x\)? \[300(1.1)^x > 200(1.2)^x \text{ when } x \leq \_ \_ \_ \] (ii) For what x-values is \(300(1.1)^x < 200(1.2)^x\)? \[300(1.1)^x < 200(1.2)^x \text{ when } x \geq \_ \_ \_ \] **eTextbook and Media** **Hint** **Save for Later** **Attempts: 2 of 3 used**
Transcribed Image Text:Using the points in the graph from part (a), determine the following. Enter only integer values corresponding to the points from part (a) in the answer fields. (i) For what x-values is \(300(1.1)^x > 200(1.2)^x\)? \[300(1.1)^x > 200(1.2)^x \text{ when } x \leq \_ \_ \_ \] (ii) For what x-values is \(300(1.1)^x < 200(1.2)^x\)? \[300(1.1)^x < 200(1.2)^x \text{ when } x \geq \_ \_ \_ \] **eTextbook and Media** **Hint** **Save for Later** **Attempts: 2 of 3 used**
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