Part of the problem here is that area increases so dramatically with relatively small increases in dimensions.
For instance, a 5x7 print is 35 square inches. If you increase that size by just one inch in every direction--make it 7x9--you add another 28 sq. in., almost (not quite) doubling the area. That means almost (not quite) doubling the amount of pixels you need to cover that area. So small increases in dimensions mean you need large additional numbers of pixels to cover the increase in print area. --Mike
