Weston,Inc.,produces widgets.To manufacture a new type of widget,it took 24 iterations before the process reached a steady state of 14 hours.If Weston has a 95% learning rate,use the logarithmic approach to calculate the time it took to manufacture the first widget.
A)17.96 hours
B)17.04 hours
C)16.11 hours
D)17.71 hours

Question

Quizplus · Accepted Answer

The time to manufacture the first widget can be calculated using the learning curve formula: $T_n = T_1 \times n^{\log_b(a)}$, 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 (in decimal form), and $b$ is the base of the learning curve (usually 2 for a 90% learning curve, indicating a 10% reduction in time with each doubling of production). For a 95% learning rate, $a = 0.95$, and we're solving for $T_1$ given $T_{24} = 14$ hours.Rearranging the formula to solve for $T_1$ and substituting the given values, we get:$$14 = T_1 \times 24^{\log_2(0.95)}$$Solving for $T_1$ gives approximately 17.71 hours.