chuck,
it all depends on 2 factors. a - your original file (pixel dimensions, format, compression level, color and bit depth) and the exported file (pixel dimensions, format, compression level, color and bit depth).
just as an example - if you take a quite strongly compressed jpg (lets say at 5) and export it to be a less compressed jpg (10 to 12), the file size in kb will be larger, while maintaining the same amount of pixels. what has changed is the way the information are stored within the jpg +(to say it very simplified and without going into details about compression and possible loss of data etc)+.
if you'd take a high-res 16-bit tif and export it (again at exact same pixel dimensions) as jpg, you'd get a much smaller file, still the same pixels (at least the amount of pixels, however perhaps "lower quality" pixels, depending on compression level, original image, noise, tonality etc etc).
long (technical) story short: there is no real "one answer fits all" because it heavily depends on your original image. as a rule of thumb however, print files should be in 300 dpi and images for the web in 72.
in terms of color and bit depth it now depends who you're sending the files to. if you send them to your client, use 8 bit sRGB. if you send it to a graphic designer, i'd send him 16-bit tif files in adobe rgb. all of this makes no sense if your original image was a heavily compressed 8 bit sRGB jpg of course.