To determine the correct exponential equation, we need to analyze the given options and the characteristics of the graph in question. Since I can't see the graph, I'll provide guidance on how to approach it.
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Identifying the Y-Intercept: The Y-intercept is the value of y when x = 0. If you have the Y-intercept from the graph, you can find which option matches it.
- For an exponential function of the form \( y = a \cdot b^x \):
- The Y-intercept is equal to \( a \).
- For an exponential function of the form \( y = a \cdot b^x \):
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Growth Factor: For the exponential growth, check the base (the number being raised to the x power). The options you have are:
- \( 27 \)
- \( \frac{2}{7} \)
- \( 72 \)
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Exponential Rate of Change: Identify how steeply the graph rises or falls to help choose between the growth rates.
Analysis of Options
- Option 1: \( y = 7(27)^x \)
- Option 2: \( y = 49(27)^x \)
- Option 3: \( y = 49(\frac{2}{7})^x \)
- Option 4: \( y = 49(72)^x \)
Steps to identify the correct equation:
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Check the Y-intercept:
- If the Y-intercept is 7, pick options 1 or 3.
- If it is 49, pick options 2 or 4.
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Determine the growth rate:
- If the graph shows exponential growth, options 1, 2, or 4 could be correct.
- If it shows decay, option 3 is likely.
If you provide the Y-intercept and any additional characteristics of the graph (like growth/decay), I can help you pinpoint the correct option further!