1. The problem asks to identify which graph corresponds to the function $$y=3\left(\frac{1}{2}\right)^x$$. 2. The function is an exponential decay because the base $$\frac{1}{2}$$ is between 0 and 1. 3. The initial value (when $$x=0$$) is $$y=3\left(\frac{1}{2}\right)^0=3\times 1=3$$. 4. The graph should be a decreasing exponential curve passing through the point $$(0,3)$$ and approaching $$y=0$$ as $$x\to \infty$$. 5. From the description: - Graph a is a decreasing exponential curve passing through about $$(0,3)$$ and approaching $$y=0$$. - Graph b is a decreasing exponential curve passing through $$(0,1)$$ and approaching $$y=-2$$. - Graph c is an increasing exponential curve passing through $$(0,3)$$. - Graph d is an increasing exponential curve passing through $$(0,1)$$. 6. Therefore, the function $$y=3\left(\frac{1}{2}\right)^x$$ corresponds to graph a. Final answer: **a**