The problem asks us to analyze the given exponential function $y = 5 \cdot (\frac{1}{2})^x$ and graph it on the provided coordinate plane.

1. Problem Description

The problem asks us to analyze the given exponential function $y = 5 \cdot (\frac{1}{2})^x$ and graph it on the provided coordinate plane.

2. Solution Steps

To graph the function $y = 5 \cdot (\frac{1}{2})^x$, we can first find some points by substituting different values of $x$ into the equation.

When $x = 0$, $y = 5 \cdot (\frac{1}{2})^0 = 5 \cdot 1 = 5$. So, the point (0, 5) is on the graph.

When $x = 1$, $y = 5 \cdot (\frac{1}{2})^1 = 5 \cdot \frac{1}{2} = 2.5$. So, the point (1, 2.5) is on the graph.

When $x = 2$, $y = 5 \cdot (\frac{1}{2})^2 = 5 \cdot \frac{1}{4} = 1.25$. So, the point (2, 1.25) is on the graph.

When $x = -1$, $y = 5 \cdot (\frac{1}{2})^{-1} = 5 \cdot 2 = 10$. So, the point (-1, 10) is on the graph.

When $x = -2$, $y = 5 \cdot (\frac{1}{2})^{-2} = 5 \cdot 4 = 20$. So, the point (-2, 20) is on the graph.

Plot these points on the graph and draw a smooth curve through them. This curve represents the exponential function.

3. Final Answer

The graph is a decreasing exponential curve that passes through the points (0, 5), (1, 2.5), (2, 1.25), (-1, 10), and (-2, 20).