1. **State the problem:** Rewrite the equation $y = 4.6(0.6)^x$ in terms of base $e$ and express the answer using a natural logarithm. 2. **Recall the formula:** Any exponential expression with base $a$ can be rewritten as $a^x = e^{x \ln(a)}$ where $\ln$ is the natural logarithm. 3. **Apply the formula:** Rewrite $0.6^x$ as $e^{x \ln(0.6)}$. So, the equation becomes: $$y = 4.6 e^{x \ln(0.6)}$$ 4. **Evaluate the natural logarithm:** Calculate $\ln(0.6)$. Using a calculator, $\ln(0.6) \approx -0.511$ (rounded to three decimal places). 5. **Rewrite the equation with the evaluated logarithm:** $$y \approx 4.6 e^{-0.511x}$$ **Final answer:** $$y \approx 4.6 e^{-0.511x}$$ This expresses the original function in terms of base $e$ with the natural logarithm evaluated and rounded.