Final answer:
The function f(x) = 7(1/3)^x represents an exponential decay because the base (1/3) is less than 1, and thus the function's values will decrease as x increases.
Step-by-step explanation:
The function f(x) = 7(1/3)^x represents an exponential decay graph. This is because the base of the exponential function, (1/3), is less than 1. An exponential decay situation is one where values decrease rapidly at first and then level off to approach zero as time goes on. In contrast, exponential growth would require a base greater than 1, where values increase rapidly as x increases.
To illustrate, in case of exponential decay, if we plot the graph with successive values of x, we would see the curve starting from a certain y-value when x is 0 (in this case, y=7), and as x increases, the y-value decreases towards zero but never actually reaches it.
Moreover, since the base (1/3) is constant and less than 1, the function's values will decrease exponentially, hence option B) Exponential decay is the correct choice.