According to Page 170 of the owner's manual you should get the following resolutions:

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Now, if I understand this correctly, DPI is dots per inch and whether it's 300DPI or 72DPI will depend upon how big the resulting photo is when it is displayed or printed. If you print the photo on a 4x6 and you do not lose any of the pixels then you are going to get

4368 / 6 = 728 DPI horizontal resolution
2912 / 4 = 728 DPI vertical resolution

So you are at 728 DPI.

That same photo printed at 8 x 12 will get you

4368 / 12 = 364 DPI horizontal resolution
2912 / 8 = 364 DPI vertical resolution

This is 364 DPI.

Remember, no matter what we do the image only has 4368 horizontal dots and 2912 vertical dots. The more inches that it's spread across the smaller the DPI.

Computer screens are generally 72 DPI because that's the largest number of pixels they can fit into 1 inch worth of screen "real estate". Note that newer monitors can go higher (96 and 120) and you can see the DPI of your screen in the advanced display properties (in Windows).

To make a long story short, you might be seeing the display properties of your image showing 72 DPI because it's being displayed on your monitor which really has little to do with the DPI of the image since that is completely dependent upon how big it is when you print it.