convert - Dimensional analysis/conversion problem: Map scale to image resolution (dpi)

Given a map scale of 1:17,200 and a raster whose cell size is 6 inches, what resolution (dots per inch) should I choose when exporting the map to an image in order to maintain the raster's native resolution (1 cell = 1 dot). Need a quick refresher on the conversion formulas.

Answer

I found this formula on the ESRI Mapping Center Blog:

1/x = 1 / (pixel ground size [m/pixel] × pixel density [pixels/m]), so that 1 meter on the map represents x meters on the ground

Which, rearranged to solve for pixel density (resolution) is:

pixel density [pixels/m] = x / pixel ground size [m/pixel]

Plugging in my numbers/units this is:

pixel density [pixels/inch] = 17,200 / 6 inches = 2866.67 pixels/inch

That's going to be a big file...