over which interval does the exponential show a more rapid rate of change? 0<x<1 0<x<2 1<x<2

Answer:

C. (1 < x < 2)

Explanation:

Step1: Recall rate - of - change concept

The rate of change of a function (y = f(x)) over an interval ([a,b]) is given by (\frac{f(b)-f(a)}{b - a}). For an exponential function, we can also visually assess the steepness of the curve over different intervals.

Step2: Analyze the intervals

For the interval (0<x<1), the exponential curve is increasing but not as steep as in other intervals. For the interval (0 < x<2), it includes the less - steep part from (0<x<1). For the interval (1<x<2), the exponential curve is much steeper compared to the previous intervals. The steeper the curve of a function over an interval, the greater the rate of change. So the exponential shows a more rapid rate of change over the interval (1 < x < 2).