A trainee in a computer company takes 0.9 times as long to assemble each computer as he took to assemble the preceding computer. If it took him 30 minutes to assemble the first computer, find the total time he takes to assemble the first five computers (round to the nearest minute).
A) 123 minutes
B) 122 minutes
C) 221,430 minutes
D) 103 minutes
The time it takes the trainee to assemble each computer follows a geometric sequence with a common ratio of 0.9. To find the total time it takes to assemble the first five computers, we can write out the terms of the sequence and add them up.
The first term is 30 minutes.
The second term is 0.9 * 30 minutes.
The third term is 0.9^2 * 30 minutes.
The fourth term is 0.9^3 * 30 minutes.
The fifth term is 0.9^4 * 30 minutes.
To find the total time, we can add up all these terms.
Total time = 30 + 0.9 * 30 + 0.9^2 * 30 + 0.9^3 * 30 + 0.9^4 * 30
Using the formula for the sum of a geometric series, we can simplify this expression.
Total time = 30 * (1 - 0.9^5) / (1 - 0.9)
Calculating this expression:
Total time = 30 * (1 - 0.59049) / 0.1
Total time = 30 * (0.40951) / 0.1
Total time = 122.85 minutes
Rounding to the nearest minute, the total time is 123 minutes.
Therefore, the correct answer is:
A) 123 minutes.