Exponential decay is characterized by a base that is between 0 and 1. In the context of your equations, this means we are looking for equations that have a fraction less than 1 raised to the power of \(x\).
Let's analyze each equation:
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\(y = 6 \cdot 7^x\) - This represents exponential growth because \(7 > 1\).
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\(y = 4 \cdot \left(\frac{7}{8}\right)^x\) - Here, \(\frac{7}{8}\) is less than 1, indicating exponential decay.
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\(y = 4 \cdot 2^x\) - This represents exponential growth because \(2 > 1\).
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\(y = 2 \cdot \left(\frac{3}{1}\right)^x\) - This simplifies to \(y = 2 \cdot 3^x\), which is also exponential growth since \(3 > 1\).
Thus, the equation that models exponential decay is:
\(y = 4 \cdot \left(\frac{7}{8}\right)^x\).