The rate of decay of certain substance is directly proportional to the amount present at that instant. Initially, there are 27 gms of certain substance and 3 hours later it is found that 8 gms are left, then the amount left after one more hour is

Step-by-step solution

(C) Let x gms be the amount of the substance left at time t . Then the rate of decay be d x d t , which is proportional to x . array l dx dt x dx dt =- k x , where k >0 1 x d x = - k dt x =- kt + c Initially i.e. when t =0, x =27 . 27=- k 0+ C C = 27 x =- kt + 27 x - 27=- kt Now, when t =3, x =8 array array l ( 8 27 )=-3 k -3 k = ( 2 3 )³=3 ( 2 3 ) k =- ( 2 3 ) ( x 27 )= t ( 2 3 ) When t =4, ( x 27 )=4 ( 2 3 )= ( 2 3 )⁴ x 27 = 16 81 x = 16 3 gms array