Suppose that a company has recently started manufacturing a new line of helicopters, and it took 106.496 labor days to complete the 16th helicopter. if the learning rate is 80%, how many days did it take to complete the 1st helicopter?

a. 978.7

b. 426

c. 1703.9

d. 260

e. 208 f. 43.6

A "learning rate" expresses the ratio of the labor spent on the n-th item to that spent on the (n/2) - th item. That is, the 8th helicopter manufactured took days related by ...

0.8 * (days for 8th) = (days for 16th)

(days for 8th) = (days for 16th) / 0.8 = 1.25 * (days for 16th)

Then the days for the 4th are 1.25 times that, and the days for the 2nd are 1.25 times the days for the 4th. The days for the first helicopter will be

... 1.25⁴*106.496 days = 260 days

The appropriate choice is

... d. 260