OurWorkbench

Actually, the serial number 7830008 (it happens frequently that a digit is dropped when looking up serial numbers) is a 15k from the end of 1887 or probably early 1888 and made in Clydebank Kilbowie per https://ismacs.net/singer_sewing_mac...-2-9-2024.html
My guess is that it is a 15K3 as at one time I believe it had Tiffany or Gingerbread decals, which are my favorite and would have multiple colors, besides the gold. Some are more blue and some are more pink. https://ismacs.net/singer_sewing_mac...ic-decals.html
I am thinking that if it is a 15K3, it will have what is considered a long beak shuttle. The picture looks like it may have a motor (or hand crank) boss on it which would be under the hand wheel. I didn't think that they made the motor boss that early.
There is some info about 15 class machines at https://cyndykitt.com.au/machines/info-15.htm and shows the long beak shuttle which would be like the 15-1 machines. Usually the machines made in USA and Kilbowie had the same variety numbers, but not for the 15s.

I think that it looks in pretty good shape, especially for the age. It is suggested that simple cleaning the machine with sewing machine oil, is best for these old machines. Some have used Glenn's method as shown at Cleaning and repairing the Shellac clear coat on Vintage sewing machine heads