over which interval does the exponential show a more rapid rate of change?\no 0<x<1\no 0<x<2\no 1<x<2\no…

Explanation:

Step1: Recall rate - of - change concept

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. For an exponential function, a steeper graph indicates a more rapid rate of change.

Step2: Analyze each interval visually

• For $- 2<x<0$: The exponential function is increasing slowly.
• For $0<x<1$: The function is increasing, but not as steeply as in some other intervals.
• For $0<x<2$: This is a larger interval. We can break it down further.
• For $1<x<2$: The exponential function has a very steep slope in this interval compared to the others. The graph rises more sharply over the interval $1 < x<2$ than over the other given intervals.

Answer:

$1<x<2$