Question 6: The Dum-Dum twins run their operation for a few months. They process

Question

Question 6:
The Dum-Dum twins run their operation for a few months. They process about the same number of orders per day. After 15 days they notice that instead of taking a total of 6 minutes of processing time, it now takes 3 minutes. Fred is confused by this and asks, “how can this be?" Ethel, explains that some sort of learning effect seems to be taking place. She argues that sometimes T(n)=a*n^(-b) where T(n) is the time it takes to do jobs on the n’th day and “a” is how long it took to do jobs on the first day (6 minutes in this case). However, she does not know how to find b. Fred asserts that since time has been cut in half after 15 days, then b is ½ divided by 30. Lucy argues that Fred is still a Dum-Dum and that b is simply 30 times 50%.

a. Which one (if either) is correct?
b. What is the value of b in this setting?
c. At this rate of learning, how many days will it take until processing times drops to2
minutes?

Explanation / Answer

a. none
b. b=log215

c. n=31/b=3log215

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