Final answer:
The average rate of change for an exponential function like f(w) = 500 ⋅ 2w can be a reasonable measure in early weeks after publication which are domains 0 ≤ w ≤ 2 and 0 ≤ w ≤ 7. So, the correct choices are (a) and (b).
Step-by-step explanation:
The function described by f(w) = 500 ⋅ 2w represents an exponential growth model which shows how the number of book copies sold increases over time, specifically weeks after publication. The average rate of change of this function can give us a measure of how quickly sales are increasing over a certain time period. However, because the function is exponential, the average rate of change is not constant over different intervals. It's factored by the exponential growth, meaning it grows larger as w increases.
For shorter time intervals at the start of the book sales (specifically for options (a) 0 ≤ w ≤ 2 and (b) 0 ≤ w ≤ 7), the average rate of change can be a reliable measure as the exponential growth hasn't had as dramatic of an effect over these short periods. However, for (c) 5 ≤ w ≤ 7, (d) 5 ≤ w ≤ 10, or (e) 0 ≤ w ≤ 10, the average rate of change is less useful as a measure because the sales are growing quite rapidly and the rate between earlier and later weeks would differ significantly.
So, the appropriate domains where the average rate of change could be a reasonable measure for the number of books sold are:
Therefore, the correct options for the domain selection are option (a) and option (b).