Learning Curves

Hi Sir. Wondering if you could help me?

A company is developing a new product. During its expected life it is forecast that 6,400 units of the product will be sold for $70 per unit.

The direct material and other non-labour related costs are expected to be $45 per unit throughout the life of the product.

-Production is expected to be in batches of 100 units throughout the life of the product. The direct labour cost is expected to reduce due to the effects of learning throughout the life of the product.

The total direct labour cost of the first batch of 100 units is expected to be $6,000 and an 80% learning effect is expected to occur.

Fixed costs specific to this product are expected to be $60,000 in total for the life of the product.

Note: The value of the learning index for an 80% learning curve is –0.3219.

Question_ Calculate the total direct labour cost of the first 800 units

Solution:

Ok so since they are asking for the first 800 units, I used a tabular method.

Units time taken no of batches total
100 6000 1 6000
200 6000*80%=4800 2 9600
400 4800*80%=3840 3 15,360
800 3840*80%=3072 4 24,576

therefore the total cost for the first 800 units is 24.576. Which is correct.

The question then goes on to say calculate the total cost for the first 6400 units.

I then attempted to use the formula

y= ax^b

where a= 6000
b= 6400
b= -0.3219

however the answer I get is wrong? If I could not use the table hoe would I find the cost for the first 6400 units?

thanks