Assuming that a typical popular music CD comprises 12 songs each of 8500 KB, what would the effective transmission speed need to be capped at in order to extend the download time to 2 hours? Express your final answer in bits per second, using scientific notation correct to two decimal places
To determine the effective transmission speed, we need to calculate the total size of the music CD and divide it by the desired download time. Here's how to do it:
1. Calculate the size of the CD:
- Each song is 8500 KB.
- Since there are 12 songs on the CD, the total size would be:
8500 KB/song * 12 songs = 102,000 KB.
2. Convert the size to bits:
- Since 1 byte is equal to 8 bits, we need to multiply the size in KB by 8:
102,000 KB * 8 = 816,000 bits.
3. Convert the download time from hours to seconds:
- Since there are 3600 seconds in an hour, we multiply the download time by 3600:
2 hours * 3600 s/hour = 7200 seconds.
4. Calculate the effective transmission speed:
- Divide the size of the CD in bits by the download time in seconds:
816,000 bits / 7200 seconds = 113.33 bits per second.
Therefore, the effective transmission speed needs to be capped at approximately 113.33 bits per second, expressed in scientific notation as 1.13 x 10^2 bits/s.