Final answer:
This question involves calculating the average rate of change for the function H(x)=3(2)^x over two different intervals and comparing these rates to determine how many times one is greater than the other.
Step-by-step explanation:
The student is asking about the average rate of change of a function over two different intervals, also known as sections, and how to compare these rates of change. The function given is H(x) = 3(2)^x, and we are to evaluate this for section 8 (from x=12 to x=2) and section B (from x=32 to x=4). The average rate of change of a function over an interval [a, b] is found by calculating the difference in the function's values at these points, H(b) - H(a), and dividing it by the difference in the points, b - a. To determine how many times greater the average rate of change of section B is than section 8, we simply divide the average rate of change of section B by that of section 8.
However, the values provided in the question appear to contradict the typical interpretation of the mathematical concept of average rate of change since they suggest that x is decreasing from a higher value to a lower value, which is not a standard approach. If we consider 'section 8' to be from x=2 to x=12 and 'section B' to be from x=4 to x=32, we could then calculate the average rates of change correctly.