If a worker takes 50 hours to perform a task the first time he/she does it, and the learning percentage is 80% a. How long does it take the worker to do the task the third time it is performed?
b. How long does it take the worker to do all three tasks?
c. How much longer would it take the worker to complete two additional tasks (beyond the first three)?

Requirement a. 35.11 Hrs

Requirement b. 125.105 Hrs

Requirement c. 61.782 Hrs

Explanation:

The formula to calculate the learning curve is as under:

Y = aX^2

Here

X is cumulative number of units

Y is cumulative time required for X number of units

a is the time taken for first unit which is 50 hours

b = Log of Learning Curve Percentage / Log 2

Learning Curve Percentage is 80%

This means

b = log 0.8 / log 2 = – 0.322

Requirement A: How long does it take the worker to do the task the third time it is performed?

Now in this case, X is 3 units, Y is unknown, a is 50 hours and b is 80%. By putting the values in the above formula, we have:

Y = 50 Hrs * 3 Units ^-0.322  = 125.105 Hours

Now this Y is cumulative time for unit 1, 2 and 3.

We

Time required for 3rd unit = Y for 3 cumulative units  -  50 Hrs for first Unit - Time required for second Unit

Time required for 3rd unit = 125.105 Hours  - 50 Hours - 50 Hrs * 2 Units ^-0.322  = 35.11 Hrs

Requirement B:

125.105 Hours are required to work for 3 Units (Calculated above).

Requirement C:

Cumulative time taken for 5 Units = Y = 50 Hrs * 5 Units ^-0.322 = 186.887

Now

Time taken for 4th and 5th units = Cumulative time for 5 Units   -  Cumulative time taken for 3 Units

By putting values, we have:

Time taken for 4th and 5th units = 186.887 Hrs - 125.105 Hrs = 61.782 Hrs

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