B. He wondered how many people could trace their ancestry back to nobility.
Explanation:
Trace has more than one meaning but only B. is grammatically correct and using trace how it's supposed to be used. (You can also read the sentences and see how A. is harder to read since trace could be used but isn't properly being used and C. doesn't make sense.)
The growth of technology on the way people communicate has changed because now we have phones and computers. We also have high tech watches and cars. This type of technology will change in the future because we will soon have flying cars, More advanced phones, etc.