Question

A new machine tool is brought into a production line to help speed production. You take 200 seconds to produce the first widget. By the 400th widget, you reduce the time to only 15 seconds. What is "b" in the formula Tn=T1nb for the learning curve (round to the nearest three decimals)?

a. -0.898
b. 0.454
c. -0.432
d. 0
e. 17

Please explain why

Answer 1

Answer: I think the answer is b

Answer 2

c. -0.432

Explanation:

The given formula is

`T_(n)=T_(1)(n)^(b)`

Where
`T_(1)=200`,
`T_(n) =15` and
`n=400`. (givens of the problem).

Replacing and solving for
`b` , we have

`15=200(400)^(b) \\(400)^(b) =(15)/(200)= 0.075\\log((400)^(b) )=log(0.075)\\b(log(400))=log(0.075)\\b=(log(0.075))/(log(400))\\ b \approx -0.432`

Therefore, the right answer is c.