Question

The function, f , gives the number of copies a book has sold w weeks after it was published. The equation f ( w ) = 500 ⋅ 2 w defines this function. Select all domains for which the average rate of change could be a good measure for the number of books sold. Group of answer choices

a. 0 ≤ w ≤ 2
b. 0 ≤ w ≤ 7
c. 5 ≤ w ≤ 7
d. 5 ≤ w ≤ 10
e. 0 ≤ w ≤ 10

Answer 1

The most appropriate domain for calculating the average rate of change for the function describing the number of books sold is 0 ≤ w ≤ 2.The correct answer is option a.

Step-by-step explanation:

The student is asking about selecting appropriate domains for calculating the average rate of change for a function describing the number of books sold over time. In the given function f(w) = 500 ⋅ 2w, since it is an exponential function, the average rate of change will increase drastically for higher values of w. Therefore, domains with smaller intervals, especially near the beginning of the function, will have a more stable average rate of change than those with larger intervals or those further along the w axis.

Here are the options analyzed:

• 0 ≤ w ≤ 2 is a good domain as it is right after the book's release and the average rate of change would be less volatile.
• 0 ≤ w ≤ 7 spans a longer period, potentially showing a more unpredictable average rate of change due to the function's exponential nature.
• 5 ≤ w ≤ 7 and 5 ≤ w ≤ 10 are less ideal for calculating an average rate since that is further out and the rate of change could be quite high.
• 0 ≤ w ≤ 10 shows the most drastic change and would be less meaningful for an average rate of change.

The most appropriate choices for calculating the average rate of change for the function f(w) to approximate the number of books sold would be 0 ≤ w ≤ 2.