The assets of a person are increasing at a rate proportional to the square root of the assets at a given time. His assets increase from Rupees 9 crores to Rupees 16 crores in 2 years, then his assets at the end of 5 more years will be

Step-by-step solution

aligned & dx dt x & dx dt = k x & dx x = kdt & 2 x = kt + C aligned When t =0, x =9 i.e. 2 9 = k 0+ C aligned & c =6 & 2 x = kt +6[ Putting c =6] & When t =2, x =16 i.e. 2 16 = k 2+6 k =1 & 2 x = t +6 [Putting k =1] aligned After 5 years at t=7 aligned & 2 x =7+6 & x =6.5 & x=42.25 aligned