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

Answer 1

Answer:

b = - 0.432

Step-by-step explanation:

It takes 200 seconds to produce the first widget. And by the 400th widget, it takes only 15 seconds.

Now, the formula that gives the time to make the nth widget is given by

$T_{n} = T_{1} (n)^{b}$ and we have to evaluate the constant b from the above-given conditions.

So, $15 = 200(400)^{b}$

⇒ $400^{b} = 0.075$

Taking log on both sides

b log (400) = log (0.075)

⇒ b = - 0.432 (Answer)