Question
Which option is the correct exponential equation for the graph?
Option #1: y=2(3)x
Option #2: y=−2(3)x
Option #3: y=3(2)x
Option #4: y=3(6)x
(1 point)
Option #
is the correct equation for the graph.
Remaining Attempts : 3
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Answers
GPT-4o mini
To correctly determine which option is the right exponential equation for the graph, I would need to see the graph itself or have specific details about its characteristics, such as the y-intercept, the growth/decay factor, and any notable points (like maximum or minimum values).
However, I can guide you on how to evaluate each option to choose the right one based on common characteristics of exponential functions:
1. **Identify the base**: Exponential functions have a form y = a(b)^x where 'a' is a constant (the y-intercept) and 'b' is the base (growth factor if b > 1, decay factor if 0 < b < 1).
2. **Determine if the function is growing or decaying**: If the output increases as x increases, it signifies growth, which typically means the base (b) is greater than 1. If the output decreases, it represents decay.
3. **Check for negative values**: If there are negative outputs, consider if the constant (a) in front of the function is negative.
Based on the options:
- **Option #1: y = 2(3)^x** (exponential growth)
- **Option #2: y = -2(3)^x** (exponential decay, reflects over the x-axis)
- **Option #3: y = 3(2)^x** (exponential growth)
- **Option #4: y = 3(6)^x** (exponential growth, faster than option #3)
Please analyze the graph in regard to these points, and if you can describe the shape or any critical features, I would be able to help narrow it down further!
However, I can guide you on how to evaluate each option to choose the right one based on common characteristics of exponential functions:
1. **Identify the base**: Exponential functions have a form y = a(b)^x where 'a' is a constant (the y-intercept) and 'b' is the base (growth factor if b > 1, decay factor if 0 < b < 1).
2. **Determine if the function is growing or decaying**: If the output increases as x increases, it signifies growth, which typically means the base (b) is greater than 1. If the output decreases, it represents decay.
3. **Check for negative values**: If there are negative outputs, consider if the constant (a) in front of the function is negative.
Based on the options:
- **Option #1: y = 2(3)^x** (exponential growth)
- **Option #2: y = -2(3)^x** (exponential decay, reflects over the x-axis)
- **Option #3: y = 3(2)^x** (exponential growth)
- **Option #4: y = 3(6)^x** (exponential growth, faster than option #3)
Please analyze the graph in regard to these points, and if you can describe the shape or any critical features, I would be able to help narrow it down further!