Appendix A: Learning Curves in the BAII Plus

The BAII Plus calculator can be used for more than just Business Math.  For example, we use power functions to understand learning Curves.

Example A.1

In manufacturing a certain part, we find that the initial part takes 176 hours to manufacture, and that there is a 90% learning curve.

1. Find a power function that shows the time to create the nth item as a function of n.
2. How much time does it take to manufacture the 144th item?
3. How many items to we need to manufacture before we are down to 50 hours per part?

We are looking for a function of the form:

[latex]t_n = t_1 n^b[/latex]

or using your calculator’s built in notation [latex]y = ax^b[/latex]

We can find this using the Data worksheet on the calculator, by fitting a power function using the data points given: (1, 176) and (2, 176×0.9)

1. We have found a and b in the calculator, so we know that we have: [latex]t_n = 176 n^{-0.152003093}[/latex]
2. The 144th item takes 82.69 hours to manufacture
3. It will take around 50 hours to manufacture the 3941^st item.

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