Which is an exponential decay function? \( f(x)=\frac{3}{4}\left(\frac{7}{4}\right)^{x} \) \( f(x)=\frac{2}{3}\left(\frac{4}{5}\right)^{-x} \) \( f(x)=\frac{3}{2}\left(\frac{8}{7}\right)^{-x} \) \( f(x)=\frac{1}{3}\left(-\frac{9}{2}\right)^{x} \)

An exponential decay function has the general form: \[ f(x) = a \cdot b^x \] where: - \( a \) is a constant. - \( 0 < b < 1 \) ensures that the function decreases as \( x \) increases. Let's analyze each function: 1. **\( f(x) = \frac{3}{4}\left(\frac{7}{4}\right)^x \)** - **Base:** \( \frac{7}{4} > 1 \) - **Conclusion:** This function represents exponential growth, not decay. 2. **\( f(x) = \frac{2}{3}\left(\frac{4}{5}\right)^{-x} \)** - **Rewriting the base:** \( \left(\frac{4}{5}\right)^{-x} = \left(\frac{5}{4}\right)^x \) - **Base:** \( \frac{5}{4} > 1 \) - **Conclusion:** This function represents exponential growth, not decay. 3. **\( f(x) = \frac{3}{2}\left(\frac{8}{7}\right)^{-x} \)** - **Rewriting the base:** \( \left(\frac{8}{7}\right)^{-x} = \left(\frac{7}{8}\right)^x \) - **Base:** \( \frac{7}{8} < 1 \) - **Conclusion:** This is an **exponential decay** function. 4. **\( f(x) = \frac{1}{3}\left(-\frac{9}{2}\right)^x \)** - **Base:** Negative base (\( -\frac{9}{2} \)) can cause oscillations and is not typical for standard exponential decay functions. - **Conclusion:** This does not represent a standard exponential decay function. **Therefore, the exponential decay function among the given options is:** \[ f(x) = \frac{3}{2}\left(\frac{8}{7}\right)^{-x} \] **Final Answer:** \( f(x)=\frac{3}{2}\left(\frac{8}{7}\right)^{-x} \) is an exponential decay function.