12 grams (\text{g})(g)left parenthesis, start text, g, end text, right parenthesis of a chemical are added to a metal. The amount AAA, in grams, of the chemical remaining during a reaction with a metal plate decreases by 0.5 \, \text{g}0.5g0, point, 5, start text, g, end text per second. If instead the plate were dissolved, the amount A'A ′ A, prime, in grams, of chemical remaining would decrease by half of itself every 444 seconds. How many grams greater is AAA than A'A ′ A, prime after 121212 seconds?