Final answer:
To find the average time to produce 15 units with a learning rate of 0.9, we apply the learning curve formula, sum the times for each unit, and then divide by 15. The exact average time needs calculation using the learning curve equation and the sum of a geometric series formula.
Step-by-step explanation:
To determine the average time to produce 15 units of a product with a learning rate of 0.9, we must use the learning curve theory. The learning curve theory states that the time required to produce the nth unit is given by T(n) = T(1) * n^(log(base2)learning rate), where T(1) is the time taken to produce the first unit. For a learning rate of 0.9, we calculate the time for each unit and then find the average.
For the first unit, the time taken is 41 hours. The formula for the nth unit is then T(n) = 41 * n^(log(base2)0.9). The average time (AT) for 15 units is calculated by summing the time for each unit from 1 to 15 and then dividing by 15. The sum can be found using the formula for the sum of a geometric series:
S = a(1 - r^n) / (1 - r)
, where a is the first term, r is the common ratio, and n is the number of terms.
Unfortunately, without further details or a calculator, we cannot provide the exact numerical average. This average time would reflect the improved efficiency in producing each subsequent unit due to the learning effect.