To find the exponential equation of the form \( y = ab^x \), we can use the points provided.
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We know that the graph passes through the points \( (0, 16) \) and \( (1, 6.4) \).
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From the point \( (0, 16) \): \[ y = ab^0 = a = 16 \] So, \( a = 16 \).
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Now using the point \( (1, 6.4) \): \[ y = ab^x \Rightarrow 6.4 = 16b^1 \] This simplifies to: \[ 6.4 = 16b \] Dividing both sides by \( 16 \): \[ b = \frac{6.4}{16} = 0.4 \]
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Now we can substitute \( a \) and \( b \) back into the equation: \[ y = 16(0.4)^x \]
Thus, the exponential equation shown in the graph is: \[ y = 16(0.4)^x \]
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