Logarithms and the value of b

When y = axb in learning curve theory, the value of b = log of the learning rate/log of 2. The learning rate is expressed as a proportion, so that for an 80% learning curve, the learning rate is 0.8, and for a 90% learning curve it is 0.9, and so on.

For an 80% learning curve, b = log 0.8/log 2.

Using the button on your calculator marked ‘log'

b = -0.0969
0.3010

= -0.322

Using the formula

Suppose, for example, that an 80% learning curve applies to production of item ABC. To date (the end of June) 230 units of ABC have been produced. Budgeted production for July is 55 units.

The cost of the very first unit of ABC, in January, was $120.

Required

Calculate the budgeted total labour cost for July.