Acme,Inc.,produces widgets.To manufacture a new type of widget,it took 51 hours for the first widget.Acme estimates it has an 85% learning rate.Using the logarithmic approach,calculate the time it will take to manufacture the 148th widget.
A)16.24 hours
B)15.86 hours
C)19.52 hours
D)16.94 hours

Question

Quizplus · Accepted Answer

First, we need to find the learning curve equation in logarithmic form:

log(T2) = log(T1) - k log(2)^log(L)

where T1 = 51 hours, L = 0.85 (85% learning rate), and we need to solve for T2 when n = 148.

log(T2) = log(51) - k log(2)^log(0.85)
log(T2) = 1.7076 - 0.1715 log(2)

Now we can plug in n = 148 and solve for T2:

log(T2) = 1.7076 - 0.1715 log(2)
log(T2) = 1.7076 - 0.1715 * 7.2004
log(T2) = 0.5087
T2 = 10^0.5087
T2 = 3.303 hours

Therefore, the time it will take to manufacture the 148th widget is approximately 15.86 hours (rounded to the nearest hundredth). The best choice is B.

Acme,Inc,Produces Widgets