Save for the fact that what you have will be silver plate if the maker’s mark doesn’t include the word “sterling”, the info in post #2 is not correct.
There is a huge amount of confusion about pieces from the Rogers family and associated companies using the name (often with no family connection but the result of an endless succession of off-shoots, mergers, buy-outs etc) such that many sources misleadingly quote dates which only relate to a particular ‘Rogers’ company.
The “1847 Rogers Bros.” mark was first used in 1862, although not registered as a protected trademark until 1935. There was a second registration for the same mark, but in a bolder typeface in 1948 (that mark having first been used in 1916).
“1847 Rogers Bros.” is not a pattern. It’s a brand name, for which there are dozens of patterns pre-dating 1922 and all the way back to at least 1862… all in silver plate. The ‘1847’ part of the branding takes its cues from Rogers’ development of a process for electroplating onto base metal in that year.
The possible dating for your knife will come from a combination of the actual pattern and perhaps also the typeface style of the mark… since there were, as I said, two styles with different usage periods. If you can show decent pictures of front-of-handle pattern and rear-of-handle mark then I might be able to help more.
[For info only, “1847 Rogers Bros. Sterling” was also registered as a trademark in a script-style lettering in 1940 (it’s first year of use) and that will be Sterling silver.]