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A certain type of optical switch in a fiber-optic system allows a light signal to continue in one of two fibers. How many possible paths could a light signal follow if it passes through 600 such switches? The number of possible paths are (Use scientific notation. Do not round until the final answer. Then round to two decimal places as needed.)

Ask by Weber Murphy. in the United States
Mar 13,2025

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The number of possible paths is approximately \(4.15 \times 10^{180}\).

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With each of the 600 switches allowing for 2 possible paths (either of the two fibers), the total number of possible paths that the light signal can take can be calculated as \( 2^{600} \). Using scientific notation, we have: \[ 2^{600} \approx 1.074 \times 10^{181} \] Thus, the number of possible paths is approximately \( 1.07 \times 10^{181} \) when rounded to two decimal places. This number is astronomically large, demonstrating the incredible potential for routing information in fiber-optic networks!

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