To identify the correct exponential equation from the given options, we typically need to know the base value and the initial value (y-intercept) of the curve from the graph.
Since I can't see the graph you've provided, I can't directly derive the equation. However, I can help you understand how to analyze the points on the curve to determine the equation:
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Identify the y-intercept: If the graph passes through a specific point, say \( (0, y_0) \), then \( y_0 \) is your initial value (the coefficient in front of the exponential).
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Determine the base: Look for a second point on the curve. If you have two points—let’s say \( (x_1, y_1) \) and \( (x_2, y_2) \)—you can find the factor by which \( y \) increases as \( x \) increases. The base \( b \) can often be found using the formula: \[ b = \frac{y_2}{y_1} \text{ if } x_2 - x_1 = 1 \]
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Formulate the equation: The general form of an exponential function is \( y = a \cdot b^x \), where \( a \) is the initial value and \( b \) is the base.
Based on the structure of provided responses, you can substitute the identified \( a \) and \( b \) into the format \( y = a \cdot b^x \) to choose the correct option.
If you can provide more information about the specific points located on the graph, I would be able to assist you in narrowing down the correct option.