Final answer:
To graph the exponential decay function f(x) = 21(0.5)^x, start by plotting f(0)=21, choose subsequent x values to plot additional points, label the 'x' and 'f(x)' axes, select a suitable scale, connect the points to illustrate the declining curve, and shade areas if required for probability.
Step-by-step explanation:
To graph the function f(x) = 21(0.5)^x, we recognize that this is an exponential decay function because the base of the exponent, 0.5, is less than 1. This means as x increases, f(x) will decrease. To effectively graph this function:
- Start by plotting the point where x = 0. Since anything raised to the power of 0 is 1, f(0) = 21 * 1 = 21.
- Next, choose a few more values for x to see how the function behaves. For example, for x = 1, f(1) = 21 * 0.5 = 10.5, and so on.
- Label the axes with 'x' for the horizontal axis and 'f(x)' for the vertical axis.
- Choose an appropriate scale for both axes, keeping in mind that your x values range from 0 to 20 and the maximum y value starts at 21 (when x=0).
- Connect the points smoothly, since an exponential function is continuous. The graph will show a declining curve starting at (0,21).
- Make sure to label important points, the decay rate, and if necessary, the mean value.
Lastly, remember to shade the area under the curve if the problem requires it, such as when finding the probability that f(x) is less than a certain value.