1. **State the problem:** Identify the graph corresponding to the equation $$y = 8(4)^x$$. 2. **Recall the form of the equation:** This is an exponential function of the form $$y = a b^x$$ where $$a = 8$$ and $$b = 4$$. 3. **Important rules:** - If $$b > 1$$, the function represents exponential growth. - If $$0 < b < 1$$, the function represents exponential decay. 4. **Analyze the base:** Here, $$b = 4 > 1$$, so the function is exponential growth. 5. **Behavior of the graph:** - As $$x \to -\infty$$, $$y = 8(4)^x \to 0$$ (approaches zero but never touches). - At $$x=0$$, $$y = 8(4)^0 = 8 \times 1 = 8$$. - As $$x$$ increases, $$y$$ grows rapidly because of the base 4. 6. **Conclusion:** The correct graph is the one showing exponential growth starting near zero for negative $$x$$ and rising steeply for positive $$x$$, passing through $$y=8$$ at $$x=0$$. This matches the first and second graphs described (bottom-left and bottom-center), which show exponential growth. **Final answer:** The equation $$y = 8(4)^x$$ corresponds to the first and second graphs (exponential growth curves).