Answer:
Approximately 18 units will be produced before the output rate exceeds 12 units per hour.
Step-by-step explanation:
The learning curve formula is given by:
![Y = aX^{b}](https://tex.z-dn.net/?f=Y%20%3D%20aX%5E%7Bb%7D)
In which:
Y is the average time per unit.
X is the cumulative number of units produced.
a is the time required to produe the first unit
b = log of learning rate/log 2
In our problem, we have:
Y = 12 units per hour. We are working in minutes, what is the average time per unit?
60 minutes - 12 units
Y minutes - 1 unit
![12Y = 60](https://tex.z-dn.net/?f=12Y%20%3D%2060)
![Y = 5](https://tex.z-dn.net/?f=Y%20%3D%205)
So Y = 5.
X is the value we want to find
a = 30
b = ![\frac{log 0.65}{log 2}=-0.6215](https://tex.z-dn.net/?f=%5Cfrac%7Blog%200.65%7D%7Blog%202%7D%3D-0.6215)
So
![Y = aX^{b}](https://tex.z-dn.net/?f=Y%20%3D%20aX%5E%7Bb%7D)
![5 = 30X^{-0.6215}](https://tex.z-dn.net/?f=5%20%3D%2030X%5E%7B-0.6215%7D)
![\frac{1}{6} = \frac{1}{X^{0.6215}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B6%7D%20%3D%20%5Cfrac%7B1%7D%7BX%5E%7B0.6215%7D%7D)
![X^{0.6215} = 6](https://tex.z-dn.net/?f=X%5E%7B0.6215%7D%20%3D%206)
![\sqrt[0.6215]{X^{0.6215}} = \sqrt[0.6215]{6}](https://tex.z-dn.net/?f=%5Csqrt%5B0.6215%5D%7BX%5E%7B0.6215%7D%7D%20%3D%20%5Csqrt%5B0.6215%5D%7B6%7D)
![X = 17.86](https://tex.z-dn.net/?f=X%20%3D%2017.86)
Approximately 18 units will be produced before the output rate exceeds 12 units per hour.