You can, but you'll only expand the existing pixel info. You won't improve
the resolution of the image as it gets larger.
Just place the jpg into your document, scale it to the desired size, and
then select File>Export and select jpg (or any other file type you desire
from the list).
Is there another Adobe program that i could use to maintain the picture quality as it gets bigger?
Perhaps with Photoshop and the help of a specialized plug-in.
Here's one that I've seen in action:
Also check out Genuine Fractals here:
Photoshop by itself works as well as the plug ins or third party apps and you can enlarge with success images but this is what you should understand before doing this.
One the jpeg format is lousy which mans to some degree you lose data when you resave. The way it does it compression is the problem it uses colors that dominate an area of the file to replace neighboring pixels with the same color value, if done under certain circumstances it cause jpeg artifacts. Also if you resave the file again it will once again replace neighboring pixels beyond what it did in the first place. At first it is very subtle and often not even distinguishable until many resaves but eventually you will see the effects and then it goes rapidly down hill.
When however you open int in Photoshop pHotoshop saves you by translating it into the Photoshop format until you resave it and if you choose the jpeg format degradation occurs. Best to save a .psd or tiff which can be placed i AI as well.
Then be aware that certain files will resample better than others. Scanned images will though you do better by scanning to the higher resolution. Digital captured images do much better and often benefit from resampling to a higher res.
If your jpeg cam from a digital capture you will do better than if it was fro a scan. In either case it is best to immediately resave as a tiff or psd file then do your resample.