Nikola Motors produces a very high end car. Let us suppose it takes 686 hours of labor to produce the first batch. Because of the advanced technical parts and special handcrafted material, the learning curve is considerably lower than industry standards, the learning rate is 97%. How many hours would it take to produce the [n]th batch?
The learning curve formula is:
Hours for nth unit = Hours for first unit * (n ^ log(learning rate) / log(2))
Using this formula and plugging in the given values:
Hours for nth unit = 686 * (n ^ log(0.97) / log(2))
Simplifying with a calculator:
Hours for nth unit ≈ 686 * (n ^ -0.0318)
Therefore, to produce the [n]th batch, it would take approximately 686 times the [n]th power of 0.97, or 686 multiplied by 0.97 to the power of negative 0.0318, hours of labor.
To calculate the number of hours it would take to produce the nth batch, we can use the learning curve formula:
H(n) = H(1) * n^log(r, L)
Where:
H(n) is the number of hours it would take to produce the nth batch
H(1) is the number of hours it took to produce the first batch (686 hours)
n is the batch number
r is the learning rate (97% or 0.97)
L is the base of the logarithm (in this case, 2 because the learning curve doubles per batch)
Let's substitute the values into the formula and calculate the number of hours to produce the nth batch.
H(n) = 686 * n^log(0.97, 2)
Note: The logarithm used in this calculation is a logarithm with base 0.97 and argument 2.
Please provide the specific batch number you want to calculate the number of hours for (replace [n] with the batch number).