On RainTite​ Window's manual assembly​ line, a new employee can usually assemble their first window unit in 45 minutes. Management assumes a 85 percent learning rate.
Part 2
a. The second window will take 
  
38.12 minutes to be assembled. ​(Enter your response rounded to two decimal​ places.)

To calculate the time required to assemble the second window, we can use the learning curve formula. Given that the employee has a learning rate of 85%, the formula for determining the time required to complete the nth unit is:

\[
T_n = T_1 \times n^{\log(r)/\log(2)}
\]

Where:
- \(T_n\) is the time required to complete the nth unit,
- \(T_1\) is the time required to complete the first unit (45 minutes),
- \(n\) is the unit number (in this case, 2 for the second window),
- \(r\) is the learning rate (85%, or 0.85).

Let's calculate:

\[
T_2 = 45 \times 2^{\log(0.85)/\log(2)}
\]

I'll now compute this value for you.The time required to assemble the second window is approximately **38.25 minutes**, given the 85% learning rate.

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:
1. How does the learning curve change as the number of units increases?
2. What would the time be for the 3rd and 4th windows using the same learning rate?
3. How can the learning rate be improved for faster assembly times?
4. How does this learning curve model compare with real-world scenarios?
5. How would a different learning rate, say 90%, affect the assembly times?

**Tip:** The learning rate impacts not only the immediate tasks but also the overall productivity over time. A small improvement in the rate can lead to significant long-term time savings.

On RainTite​ Window's manual assembly​ line, a new employee can usually assemble their first window unit in 45 minutes. Management assumes a 85 percent learning rate.
Part 2
a. The second window will take 38.12 minutes to be assembled. ​(Enter your response rounded to two decimal​ places.)

Calculate the time required for a new employee to assemble the second window unit on RainTite's manual assembly line using the learning curve formula. This problem involves key mathematical concepts, such as exponential functions and the learning curve theorem. Suitable for students in Grades 10-12.

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