12 grams (g) of a chemical are added to a metal. The amount A, in grams, of the chemical remaining during a reaction with a metal plate decreases by 0.5 g per second. If instead the plate
were dissolved, the amount A', in grams, of chemical remaining would decrease by half of itself
every 4 seconds. How many grams greater is A than A' after 12 seconds?

A=12

Explanation:

4.5

The amount of chemical remaining after twelve seconds in the first reaction is:

A = 12 - 0.5(12)

= 12 - (6)

= 6

In the dissolved reaction, the amount of chemical loses half of itself every four seconds. This is the same thing as dividing by 2 every four seconds.

This is an exponential decay, so the amount of chemical divides by 4 every eight seconds, and by 8 seconds every twelve seconds. The amount remaining after twelve seconds in the second reaction is:

A' = 12/8

= 3/2

= 1.5

The difference between the amounts of chemical remaining is:

6 - 1.5 = 4.5

Therefore, A is 4.5 g greater than A' after twelve seconds.

the answer to the question is "five to eight weeks after the test date"