Answer:
To graph the function w(x) = 2 · (0.4)^x + 5, we can follow these steps:
1. Start by selecting a range of x-values over which you want to graph the function. Let's choose a range from -5 to 5 for this example.
2. Plug in each x-value from the chosen range into the equation w(x) = 2 · (0.4)^x + 5 to calculate the corresponding y-values. For example, when x = -5, the corresponding y-value is w(-5) = 2 · (0.4)^(-5) + 5.
3. Repeat this process for each x-value in the chosen range to get a set of ordered pairs (x, y). For example, if we plug in x = -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, and 5, we will get a corresponding set of y-values.
4. Plot each ordered pair on a coordinate plane, with the x-values on the horizontal axis and the y-values on the vertical axis.
5. Connect the plotted points with a smooth curve. An exponential function like this one typically has a curved shape, either increasing or decreasing depending on the base of the exponent. In this case, the base is 0.4, which is between 0 and 1. This means the graph will decrease as x increases.
Remember that graphing software or a graphing calculator can help visualize the graph more accurately, as it can generate a smooth curve connecting the plotted points.