It's simply a matter of scaling the image width and height up by the correct ratio. Not all images formats support a DPI metatag, and when they do, all they're telling your graphics software to do is divide the image by the ratio supplied.
For example, if you export a 300dpi image from Photoshop to a JPEG, the image will appear to be very large when viewed in your picture viewing software. This is because the DPI information isn't supported in JPEG and is discarded when saved. This means your picture viewer doesn't know what ratio to divide the image by and instead displays the image at at 1:1 ratio.
To get the ratio you need to scale the image by, see the code below. Just remember, this will stretch the image, just like it would in Photoshop. You're essentially quadrupling the size of the image so it's going to stretch and may produce artifacts.
Pseudo code
ratio = 300.0 / 72.0 // 4.167
image.width * ratio
image.height * ratio