One area in which popular culture has influenced the media bigtime is in music. With the dawn of social networking sites (starting with MySpace and now facebook etc.) came the dawn of a new power for us all as consumers and influencers. No longer were the media telling us who to have as number one and influencing our choices by pumping artificial money and support into pre-packaged bands and favoured artists, because we were able to put up our own music and favorite stars and add them, and vote for them or join a huge fan base. Some music stars became well-known in this way long befre the mainstream media even heard of them. They were johnnie-come-lately as they were forced to give air time to the stars we wanted to hear.
Well, there are various kinds of "media", so if you mean traditional media - TV, newspapers, magazines, then certainly one could say that media reflects popular culture simply because media is profitable based on what is popular.
But movies are also media, as is music, radio, even art in some ways. This kind of media tends to influence popular culture more than news and information media. It can reflect it too, but what is trendy, what is artistic expression, what is musical style can to some extent determine and shape popular culture.
Of course popular culture influences the media to some extent, but the media influence popular culture as well.
The media influence popular culture by helping to spread that culture around. People read about or see popular culture type things in the media and learn about them in that way.
Popular culture also affects the media, though. The media has to adapt to what people are used to. You can see this in how the mainstream media has to react to what is being said on blogs and on websites and such.
It's a 2-way street; they influence each other in a technology-driven spiral. Once upon a time it was the town crier. Now it's ipods. Minstrels have given way to the internet.
And more than speed and circulation have changed. McLuen said "the medium is the message." Homo sapiens is a social animal. This is how we make ourselves.