4. the function, f, gives the number of copies a book has sold w weeks after it was published. the equation…

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

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

Answer

Explanation:

Step1: Recall average rate of change formula

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 the function $f(w)=500\cdot2^{w}$, a good - measure of the average rate of change is when the interval is not too large (to avoid over - generalization) and not too small (to show a meaningful change).

Step2: Analyze each option

Option A: $0\leq w\leq2$

The interval is relatively small. The average rate of change will give a good indication of the growth in the early stages of book sales.

Option B: $0\leq w\leq7$

This interval shows the growth from the start ($w = 0$) to a more extended period ($w = 7$) and can give a good overall picture of the growth rate in the first 7 weeks.

Option C: $5\leq w\leq7$

This is a short interval in the later stage of the initial time - frame. It can show the rate of change in a more stable part of the early growth of book sales.

Option D: $5\leq w\leq10$

This interval is also reasonable as it shows the growth in a non - trivial part of the sales period.

Option E: $0\leq w\leq10$

This is a long interval that can give an overall sense of the growth of book sales from the start to 10 weeks.

Answer:

A. $0\leq w\leq2$, B. $0\leq w\leq7$, C. $5\leq w\leq7$, D. $5\leq w\leq10$, E. $0\leq w\leq10$