To write the correct exponential equation for the graph provided, we need to identify the characteristics of the points and the overall behavior of the exponential function.
In a typical exponential function in the form \(y = ab^x\):
- \(a\) is the initial value (or the y-intercept).
- \(b\) is the base of the exponential function, which determines the growth or decay of the function.
Without seeing the actual graph and specific coordinates for the points, I can only provide you with guidance on how to assess the options given:
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Look for the initial value \(a\) or the y-intercept on the graph. This will guide you to select the correct value of \(a\) from the options.
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Determine if the function is increasing or decreasing:
- If \(b > 1\), the function is increasing (growth).
- If \(0 < b < 1\), the function is decreasing (decay).
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Consider the coordinates of the labeled points on the curve to calculate slopes or verify against the options given.
Given that you have several options, here’s an analysis of each:
- \(y = 3(23)^x\): Suggests a growth function (base > 1).
- \(y = 3( \frac{2}{3} )^x\): Suggests a decay function (base < 1).
- \(y = 2( \frac{3}{2} )^x\): Suggests a growth function but starts with \(2\).
- \(y = \frac{3}{2}(3)^x\): Suggests a growth function, starting with \(\frac{3}{2}\).
Choose the equation most aligned with the graph’s characteristics and the exact values you can deduce from the points plotted.
If you can provide more details about the points or the behavior of the curve, I can give a more focused answer!
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