Unit times for a job exhibit a learning effect.If the 2^nd unit took 30 hours, and the 4^th unit took 21 hours, roughly how many hours would you estimate the 3^rd unit took? A)29 B)27 C)25 D)24 E)21

Question

Quizplus · Accepted Answer

To solve the problem using the learning effect formula, we can use the following formula:

Tn = k * (Nn)^x

Where Tn is the time for the nth unit, Nn is the number of units produced so far, k is a constant, and x is the learning rate.

We can use the two data points to estimate k and x:

30 = k * (2)^x
21 = k * (4)^x

Dividing the second equation by the first equation, we get:

21/30 = (4/2)^x
0.7 = 2^x
x = log2(0.7) ≈ -0.5146

Substituting x into one of the equations, we can solve for k:

30 = k * (2)^(-0.5146)
k ≈ 46.223

Now we can use the formula to estimate the time for the third unit:

T3 = 46.223 * (3)^(-0.5146) ≈ 24.6

Therefore, the answer is D, 24.

Unit Times for a Job Exhibit a Learning Effect