Acme,Inc.,produces widgets.To manufacture a new type of widget,it took 62 hours for the first widget.Acme estimates it has a 98% learning rate.Using the logarithmic approach,calculate the time it will take to manufacture the 56th widget.
A)55.18 hours
B)59.30 hours
C)64.55 hours
D)49.94 hours

Question

Quizplus · Accepted Answer

The time to produce the 56th widget can be calculated using the formula for learning curves: $T_n = T_1 \times n^{log_b(a)}$, where $T_n$ is the time it takes to produce the nth unit, $T_1$ is the time it takes to produce the first unit, $n$ is the unit number, $a$ is the learning rate (as a decimal), and $b$ is the base of the logarithm (usually 2 for a learning curve, indicating a doubling of units). Given $T_1 = 62$ hours, $a = 0.98$, and $n = 56$, we find $T_{56}$ by substituting these values into the formula. The calculation involves using the logarithm to find the rate of learning per doubling of production. The correct calculation leads to a result of approximately 55.18 hours, making option A the correct answer.

Acme,Inc,Produces Widgets