Regarding your question, some preamble:
There's a *lot* of superfluous math and ratio used in regards to print parameters. There are *two* concepts in play:
1. Scanning Pixels Per Inch (PPI)
2. Printing Dots Per Inch (DPI)
To further confuse things, the acronym DPI is sometimes employed, when describing scanning resolution, where PPI
would be "better". But, this is so wide spread it's maybe best to just go-with-the-flow, accept DPI as being applicable
to scanning resolution as well, and just keep in mind if the subject is scanning or printing.
To your question:
First, I would determine: what is the actual, practical, scanning resolution of your scanner. Looking at an Epson
brochure, the 4990 is specified as having "optical resolution" of 4800 DPI. (See what I mean? Even Epson is
expressing PPI as DPI.)
So, it's advertised as being able to scan at 4800 PPI. But, flatbed scanners in particular are notorious for having
*actual* detail resolving limits much lower than their max PPI. How much varies from model to model.
The simplest and most direct way to sort out the maximum *effective* PPI of your scanner is to test it. Set your
scanner to scan at 4800 "DPI" and scan a nice sharp, fine-grain slide with some good small detail. Then try lower
resolutions, say 3200 and 2400.
Open two output images in Photoshop. Say the 4800 and 2400 outputs. Zoom the 4800 image to 100%, centring the
zoom on some distinct detail. Repeat the exercise with the 2400 output, but zoom to 200% (this will "size" the
images the same on-screen).
Toggle back-and-forth between the two images [(ctrl) TAB on windows system]. Compare resolved detail. Repeat the
exercise with the various PPI output images. There is likely a level, somewhat lower than 48000, that offers the best
resolution. Going beyond that level will gain you little beyond large file size.
Now you have to make a decision: do you want to scan at the maximum *practical* PPI limit (say for example this is
2400 PPI), or would you accept some reduction in fine detail in order to reduce output file sizes? And will the
reduction still allow you to print the max size you want, at a decent print DPI (finally using that term in it's proper
application)?
Ok, so say you've settled on scanning at 2400 PPI, what are your image dimensions, in *pixels*, going to be?
Assuming your scanned area has dimensions of 1" by 1.5" (*roughly* the slide dimensions), at 2400 PPI, your
scanned output image will have *pixel* dimensions:
2400 pixels by 3600 pixels
How big a print can you make from that depends on the DPI you print at. In all cases:
To determine the dimension of the print, divide the pixel dimension by the Dot-Per-Inch value you will use when
printing.
For example with the 2400 pixels by 3600 pixel image:
If you print at *ONE* Dot Per Inch you could print an image 2400" x 3600". If you print at 100 DPI, you could print an
image 24" x 36". If you print at a decent practical level like 240 DPI, you could print an image 10" x 15".
Hope this helps ;)