The rate of reduction is proportional to the square root of a persons existing assets at that moment. If his assets at the beginning are 10000 and they dwindle down to 5625 in 2 years, then the person will be bankrupt in

Step-by-step solution

Let A be the assets at time t . The rate of reduction is proportional to the square root of the existing assets. dA dt = -k A Separating the variables and integrating: dA A = -k dt 2 A = -kt + C At t = 0 , A = 10000 2 10000 = -k(0) + C C = 200 At t = 2 years, A = 5625 2 5625 = -k(2) + 200 2(75) = -2k + 200 150 = -2k + 200 2k = 50 k = 25 The equation for the assets at time t becomes: 2 A = -25t + 200 For the person to be bankrupt, the assets A must be 0 . 2 0 = -25t + 200 25t = 200 t = 8 years Answer: 8 years