Step 1: we have to obtain the number of grams lost by the radioactive substance every year.
For an 18g radioactive substance,
If 9g remains after 8years, this implies that:
[tex]\frac{9}{8}\text{ grams = 1.125g of the radioactive substance is lost every year}[/tex]The number of years left to complete 12years after the 8years period is 4 years.
Since 1.125g of the radioactive substance is lost every year, this implies that:
[tex]1.125g\text{ x 4 = 4.5g will be lost for the remaining 4years period}[/tex]Therefore, the total loss for the 12 years period is :
[tex]9g+4.5g\text{ = 13.5g}[/tex]The amount of substance that will be left after 12years is:
[tex]18g-13.5g=4.500g[/tex]Hence, after 12years, 4.500g of the radioactive substance will be left.