Final answer:
For an exponential function, the interval (1, infinity) shows a more rapid rate of change as the exponential growth accelerates with larger positive x-values.
Step-by-step explanation:
The question asks about the intervals over which an exponential function shows a more rapid rate of change. Exponential functions, in general, increase more rapidly as the input value increases. Therefore, for an exponential function f(x) = a^x (where a > 1), the right side of the graph (as x increases) will show a more rapid rate of change than the left side. This points to intervals on the x-axis where x is positive, and especially where x is greater than 1, because the function's value grows more quickly as x gets larger. On the contrary, when x is negative, exponential growth slows down, and the slope of the graph of the exponential function flattens out as x approaches negative infinity.
This means that the correct answer is option c (1, infinity), since exponential functions experience an increasingly rapid rate of change the further one moves to the right along the x-axis, past the point where x=1.