In a learning curve application, 658.5 work hours are required for the third production unit and 615.7 work hours are required for the fourth production unit. Determine the value of n (and therefore s) in the equation Z U=K (u^n), where u=the output unit number; Z_=the number of input resource units to produce output unit u; K=the number of input resource units to produce the first output unit; s=the learning curve slope parameter expressed as a decimal (s=0.9 for a 90% learning curve); n=log⁡s/log⁡2 = the learning curve exponent.

Question

Janiah Oconnell

Mathematics

16 November, 18:06

In a learning curve application, 658.5 work hours are required for the third production unit and 615.7 work hours are required for the fourth production unit. Determine the value of n (and therefore s) in the equation Z U=K (u^n), where u=the output unit number; Z_=the number of input resource units to produce output unit u; K=the number of input resource units to produce the first output unit; s=the learning curve slope parameter expressed as a decimal (s=0.9 for a 90% learning curve); n=log⁡s/log⁡2 = the learning curve exponent.

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Answers (1)

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Turner Ross · Answer 1

n ≈ - 0.2336 s ≈ 0.8505

Step-by-step explanation:

We can put the given numbers into the given formula and solve for n.

658.5 = k·3^n

615.7 = k·4^n

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

658.5/615.7 = (3/4) ^n

The log of this is ...

log (658.5/615.7) = n·log (3/4)

n = log (658.5/615.7) / log (3/4) ≈ 0.0291866/-0.124939

n ≈ - 0.233607

Then we can find s from ...

log (s) = n·log (2)

s = 2^n

s ≈ 0.850506