Ironic, I just saw a set of these exact type of silver plated flatware at a goodwill store in Pleasant Hill, Ca, I could give you the address, for $99.99. I Googled it on my phone while I was there, and read enough to know better than to purchase it.
The 1847 on the flatware refers to the year that Rogers Bros actually started electroplating. So anytime you see Rogers Bros 1847, that really means it was made after that date, and it was electroplated. Most of the stuff you find was made in the 50s and 60s according to what I read. Rogers Bros was one of the very first companies to manufacture silver electroplated flatware. You can Google the information, makes for a very interesting read. I'm sorry to say though that it's definitely silver plate, but not worth much in today's market.
HOWEVER, if I were you, I would hang onto it. Silver is being consumed by industry at a 1:1 ratio to gold. And there is less silver produced than there is gold every year. At some point, silver is going to become very difficult to find, so silver prices have to go up, it is way undervalued at the present time. So what is not worth processing now, will be worth doing so at a later date.
I read an article about 3M's process to extract gold out of sea water, it's brilliant, but at the time 3M was experimenting with the process, gold wasn't at a price that made processing sea water to extract gold, cost effective. This was years ago. I just recently read another article about a company that is currently building a gold/sea water extraction system, now that gold prices are so high it's worth the effort. The same could be said of silver. So if you have anything that is silver plate, or some form of silver too expensive or not worth the time, effort and energy for you, save it, sooner or later it will be worth processing.