The assets of a person are reduced in his business such that the rate of reduction is proportional to the square root of the existing assets. If the assets were initially ₹ 10,00,000 and due to loss they reduce to ₹ 10,000 after 3 years, then the number of years required for the person to go bankrupt will be

Step-by-step solution

Let x be the asset at time t . aligned & d x dt x & ~d x dt =- k x , where k 0 & ~d x x =- kdt aligned Integrating on both sides, we get array ll & 2 x =- kt + c & When t =0, x=10,00,000 & 2 1000000 =- k (0)+ c & c =2(1000)=2000 & 2 x =- kt +2000...(i) array array ll & When t =3, x=10,000 & 2 10000 =-3 k +2000 & 2(100)=-3 k +2000 & 3 k =1800 & k =600 & 2 x =-600 t +2000...[From(i)] array Time to go bankrupt = T When t = T , x=0 aligned 0 & =-600 ~T +2000 & ~T = 2000 600 = 10 3 years aligned