Final answer:
Using the learning curve formula with an 80 percent learning rate, the time required to install the sixth swimming pool is estimated to be approximately 23.2 hours.
Step-by-step explanation:
The question involves a concept in operations management and specifically in learning curves, which is used to estimate the time reduction in repetitive tasks due to increased efficiency as one gains experience.
To find out the time required to install the sixth swimming pool given a 80 percent learning rate, we apply the learning curve formula:
Time for the nth unit = Time for the first unit × (n)^log(base 2) of the learning rate
If the time estimated to build the first pool is 36 hours, and assuming the learning rate is 80%, which is equivalent to a learning rate of 0.8, the time required to install the sixth pool is calculated as follows:
Time for the 6th pool = 36 × (6)^log(base 2) of 0.8
To calculate this, you can use logarithms:
log(base 2) of 0.8 = -0.3219 (approximately)
(6)^(-0.3219) = 0.6445 (approximately)
Therefore, Time for the 6th pool = 36 hours × 0.6445 = 23.202 hours (approximately 23.2 hours)
Thus, the estimated time required to install the sixth swimming pool would be around 23.2 hours.