learning Curve

Hi, Sir Jhon, Please clear that why and how the (r) is multiplied, didn’t understand

Question:

The first phase of production has now been completed for the new car seat. The first
unit actually took 12.5 hours to make and the total time for the first eight units was
34.3 hours, at which point the learning effect came to an end. Chair Co are planning
on adjusting the price to reflect the actual time it took to complete the 8th unit.

Required:
(i) Calculate the actual rate of learning and state whether this means that the
labour force actually learnt more quickly or less quickly than expected.

Solution:

Cumulative number Cumulative total Cumulative average
of Seats Produced Hours hours per unit

1 12.5 12.5
2 ? 12.5 x r
4 ? 12.5 x r2
8 34.3 12.5 x r3

Using algebra: 34.3 = 8 x (12.5 x r3)
4.2875 = (12.5 x r3) 0.343 = r3
r = 0.70