How to find domains for which the average rate of change could be a good measure?

Question

How to find all domains for which the average rate of change could be a good measure? For example: there is a problem like:

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

1. 0<=w<=2
2. 0<=w<=7
3. 5<=w<=7
4. 5<=w<=10
5. 0<=w<=10

Answer 1

Hi Chithu,

I'm Eddie I can help with this problem and exponential growth problems in general. ab^x is a basic exponential problem the a is the initial or starting quantity you are tracking in this example it's books but it can be animals, people, cars, or anything else. Time is used more in these problems so think of x = 0 as the initial or starting time. At time 0 the a will be your initial amount so 0 is typically your first value for x in a domain.

To find the max value you can think of information in the problem like the maximum time or amount that is possible. This problem gave minimal information so read carefully what I noticed this phrase "select all domains" is important because multiple answers are valid potentially.

The answers for this problem are 2 & 5 because they include the initial value and weeks 7 and 10 are good enough size to approximate the rate of change. Answer 1, weeks 0 to 2 may not have sufficient weeks to accurately describe the rate of change because weeks 1 or 2 could have been abnormally high or low sales days not reflecting a typical week think of a Christmas sale or summer when kids are out of school. Hopefully, this helps a lot with this and future problems if you like more help feel free to reach out have a nice day Chithu.