Coconut Leather Shoes is a new company that has just started to produce shoes made from coconut leather. They have determined that it takes a new production line employee 180 minutes to produce a pair of shoes. It takes the same employee an average of 100 minutes to produce their 8th pair of shoes. The learning rate of Coconut Leather Shoes is 82.21%. What will the average time be for an employee to produce their second pair of shoes? (Make use of the exponential function and round your answer off to the second decimal)Group of answer choicesA. 147.97 minutesB. 140.00 minutesC. 121.64 minutesD. 157.50 minutes
Question
Coconut Leather Shoes is a new company that has just started to produce shoes made from coconut leather. They have determined that it takes a new production line employee 180 minutes to produce a pair of shoes. It takes the same employee an average of 100 minutes to produce their 8th pair of shoes. The learning rate of Coconut Leather Shoes is 82.21%. What will the average time be for an employee to produce their second pair of shoes? (Make use of the exponential function and round your answer off to the second decimal)Group of answer choicesA. 147.97 minutesB. 140.00 minutesC. 121.64 minutesD. 157.50 minutes
Solution
The learning curve theory suggests that as a worker gains more experience, the time taken to complete a task decreases at a decreasing rate. This is often represented by an exponential function.
The learning rate of 82.21% means that each time the cumulative quantity of units produced doubles, the time per unit falls to 82.21% of its previous value.
In this case, the time taken to produce the first pair of shoes is 180 minutes. When the employee doubles their output (i.e., produces the second pair of shoes), the time per unit should fall to 82.21% of 180 minutes.
So, to calculate the average time for an employee to produce their second pair of shoes, we multiply the time taken to produce the first pair by the learning rate:
180 minutes * 0.8221 = 147.978 minutes
Rounding this to the second decimal place gives us 147.98 minutes.
So, the correct answer is A. 147.97 minutes.
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