To write the exponential equation of the form \( y = ab^x \), we can use the information from the two points given: (0, 8) and (1, 6).
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We know that at \( x = 0 \), \( y = 8 \). This means: \[ y = ab^0 \implies 8 = a \cdot 1 \implies a = 8 \]
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Now we can use the point (1, 6) to find \( b \). We substitute \( a = 8 \) and \( x = 1 \) into the equation: \[ y = 8b^1 \implies 6 = 8b \] To solve for \( b \), we divide both sides by 8: \[ b = \frac{6}{8} = \frac{3}{4} \]
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Now that we have both \( a \) and \( b \), we can write the exponential equation: \[ y = 8 \left( \frac{3}{4} \right)^x \]
Thus, the exponential equation shown in the graph is: \[ y = 8 \left( \frac{3}{4} \right)^x \]
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