Welcpme to TFL!
Your pistol is one of the older guns, which today are called Mark Is. When they were new, there were no "mark" anything, and still today none of the DE's I have ever seen has they "Mark" # actually on the gun.
Yours is not one of the very first .44s, the very first ones were all black. Other choices came later.
The quick way to spot a Mark I is the safety lever. Later marks have a different "shelf" on the lever.
The other identifying feature is the lack of slots in the barrel rib. The early guns used a scope mount that clamped on the barrel rib, later (new) guns use slots in the rib so the scope rings mount directly to the barrel.
Did you get anything else with the gun? box? Manual? tool?
I got my first DE in 84, a .357, and a .44 in 90. I've talked about them often over the years here on TFL, do a search and you'll find a number of threads with some good information.
IF you've never had one before, or learned much about them, there are some things you need to know before shooting.
Desert Eagles are NOT like the other 99% of semi auto pistols!!!! They have some things in common, but there are significant differences, and not just the size of the beast.
NEVER, ever, NEVER shoot cast lead bullets!!! Use only jacketed bullet ammo. I don't shoot plated bullets, either. Only jacketed. Nothing with bullet lube or exposed lead bottom.
This is because of the unique gas system the DE uses. If it gets clogged with lead, bullet lube, powder residue, it is extremely difficult to clean it out, as some parts of the gas system cannot be accessed.
SO, Jacketed ammo only, please, or at some point you could wind up with a manually operated repeater, that even you gunsmith might not be able to fix. And, the maker, WON'T!!
I know of one case, back in the late 90s, a guy had clogged up his .44 DE, the gunsmith had tried everything he knew, without success, and (with owner's approval) sent the gun back to Magnum Research.
I happened to be in the shop when he picked it up. The gun came back, with a new barrel assembly, and the BILL for the new barrel assembly. Clogging the gas system is NOT covered under their warranty. The manual tells you not to do it, so, if you do, its on your dime, even with a new gun.
Stick with JSP, JHP, or even FMJ (as long as they don't have exposed lead bases, never saw a .44 slug that did, but its common in .45s so its possible, in .44) and you won't have any trouble with clogging the gas system.
Next point, the Desert Eagle magazine needs to "float" to work best. IF you rest the gun on the mag, or "cup and saucer" grip it, you can have feed issues.
DO not shoot BLAZER ammo in the DE. NO ALUMINUM CASES.
Rims can tear off, and it might not even cycle.
Desert Eagles like to be fed full power ammunition, and don't like to fly with anything less. They LIKE the hot stuff. Mine have always done ok with my handloads, they just need to be on the warm side or hotter.
Light bullets seem to need top end loads to run well in the DE. The sights will be regulated for 240gr in the .44, and if you shoot 200s or 180s, you need to see how much difference there is. Since the .44 can do long range well, when you reach out there, the difference matters.
My best guess to your gun's age in mid 90s, because of the two tone finish.
They are unique beasts, not for everyone, and they need to be fed and cared for just right or they get balky, but its an 8+1 Full power (only) .44 Magnum that recoils less than the usual revolvers. Quite a bit less. The semi auto gas operated action accounts for some of that, and the massive weight tames the rest pretty well. IF you can hold it up!
For me, DE .44Mag recoil feels about like a snappy .45acp load in a 1911A1.
Enjoy the beast, and let us know if we can help with any questions.
Welcome to the club! And be prepared for nearly everyone (especially those who've never had one) to tell you, its too big, too heavy, not practical, can't be carried concealed, ammo costs too much, its too picky about what you have to shoot, and all kinds of other things "bad" about it.
Then take it out and play. with a little practice, you can smack steel at 200yds without too much effort.
Ok, maybe that's just me and 30+ years of practice, but I know other people who can do it too!
have fun!