Question: 2 Select the equation that has an exponential decay of \( 6 \% \) в. \( \quad f(x)=6(1.06)^{x} \) в. \( \quad f(x)=1000(6)^{x} \) в. \( \quad f(x)=10,000(0.94)^{x} \)

To identify the equation that represents an exponential decay of \( 6\% \), we need to understand how exponential decay is expressed mathematically. Exponential decay can be represented in the form: \[ f(x) = a(1 - r)^{x} \] where: - \( a \) is the initial amount, - \( r \) is the decay rate (as a decimal), - \( (1 - r) \) represents the remaining percentage after decay. For a decay rate of \( 6\% \), we have: \[ r = 0.06 \quad \text{and thus} \quad (1 - r) = 1 - 0.06 = 0.94 \] Now, let's analyze the given options: 1. \( f(x) = 6(1.06)^{x} \) - This represents exponential growth, not decay. 2. \( f(x) = 1000(6)^{x} \) - This also represents exponential growth, as the base \( 6 \) is greater than \( 1 \). 3. \( f(x) = 10,000(0.94)^{x} \) - This represents exponential decay, as the base \( 0.94 \) is less than \( 1 \). Thus, the correct equation that has an exponential decay of \( 6\% \) is: \[ \boxed{f(x) = 10,000(0.94)^{x}} \]