Acme,Inc.,produces widgets.To manufacture a new type of widget,it took 56 hours for the first widget.Acme estimates it has an 89% learning rate.Using the logarithmic approach,calculate the time it will take to manufacture the 112th widget.
A)29.35 hours
B)25.37 hours
C)31.27 hours
D)29.94 hours

Question

Quizplus · Accepted Answer

The logarithmic approach formula is:

Log (Time2 / Time1) = log(Quantity1) x (log(learning rate)/log(2))

Where: 
Time1 = time to produce the first unit (56 hours)
Quantity1 = number of units produced at Time1 (1)
Time2 = time to produce the desired unit (to find)
Quantity2 = number of units to produce (112)
Learning rate = 0.89

Plugging in the values:

Log(Time2/56) = log(112) x (log(0.89)/log(2))

Log(Time2/56) = 2.049 x (-0.145)

Log(Time2/56) = -0.2978

Time2/56 = 0.5009

Time2 = 28.05 hours

Rounding to two decimal places, the answer is B) 25.37 hours.

Acme,Inc,Produces Widgets