EXPF10  Workers hired to assemble sewing machines become more skilled with experience.  The most experienced workers can assemble 10 sewing machines per day.  The learning curves are different for different workers but they all eventually reach a peak production of 10 sewing machines per day.  A newly hired assembler learns to assemble 5 sewing machines per day after 6 working days.  How long will it take for this worker to reach 9 sewing machines per day? 

Solution: The simple learning curve model is most appropriate for this problem.  N_o = 10 is the maximum rate of sewing machine assembly.  The general equation governing the number of sewing machines assembled per day then is

The k can be determined with the information that after 6 days this particular worker can assemble 5 sewing machines per day.  Substitute N = 5 and t = 6  and solve for k.

and switching to logarithms

The specific learning equation for this worker is:

The time for this worker to achieve a rate of 9 sewing machines per day is obtained by putting in 9 for N and solving for t.

and switching to logarithms

It will take this worker 20 days to be able to assemble 9 sewing machines per day.