Final answer:
To estimate the time required to build a fifth pool, given a 75 percent learning curve, we use the learning curve formula with the initial 34 hours estimate for the first pool. The time estimate for the fifth pool involves exponentiating the unit number by the logarithmic learning rate and multiplying by the first unit's time.
Step-by-step explanation:
The question asks for the estimated time to install a fifth pool given that the first pool takes 34 hours to install and there is a 75 percent learning curve. A learning curve of 75 percent means that the time taken to produce the second unit is 75% of the time taken to produce the first unit. To calculate the time to install the fifth pool, we can use the formula for learning curves: T(n) = T(1)·n^(log(b)/log(2)), where T(n) is the time to produce the nth unit, T(1) is the time to produce the first unit, b is the learning percentage written as a decimal (0.75 in this case), and n is the unit number being produced (5 for the fifth pool).
To estimate the time required to install the fifth pool:
- First, we convert the 75% learning to decimal form: 0.75.
- Then, we calculate the learning curve rate: log(0.75) / log(2)
- Now, we apply the formula: 34 hours · 5^(log(0.75)/log(2))
- The estimation for the 5th pool time can be calculated using a calculator or appropriate software.
Since we do not have the actual computational result, it's important to carry out the calculation to provide a precise answer.