The decay rate of radio active material at any time t is proportional to its mass at that time. The mass is 27 grams when t=0 . After three hours it was found that 8 grams are left. Then the substance left after one more hour is

Step-by-step solution

Let ' x ' be the mass of the material at time ' t '. d x dt =- k x,(- ve sign indicates decay. ) d x x =- k dt |x|=- kt + c When t =0, x=27 c = 27 |x|=- kt + 27 When t =3, x=8 k = ( 3 2 ) When t =4 , we get array ll & |x|=-4 ( 3 2 )+ 27 & |x|= ( 16 3 ) & x= 16 3 grams array