The assets of a person reduced in his busines | vedclass

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(B) Let $A(t)$ be the assets at time $t$. The rate of reduction is proportional to the square root of the assets,so $\frac{dA}{dt} = -k\sqrt{A}$,where

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$\frac{10}{3}$ years

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(B) Let $A(t)$ be the assets at time $t$. The rate of reduction is proportional to the square root of the assets,so $\frac{dA}{dt} = -k\sqrt{A}$,where $k > 0$.Separating variables,we get $A^{-1/2} dA = -k dt$.Integrating both sides,we get $2\sqrt{A} = -kt + C$.At $t = 0$,$A = 10,00,000$. Thus,$2\sqrt{10,00,000} = C \implies C = 2 	imes 1000 = 2000$.So,$2\sqrt{A} = -kt + 2000$.At $t = 3$,$A = 10,000$. Thus,$2\sqrt{10,000} = -3k + 2000 \implies 200 = -3k + 2000 \implies 3k = 1800 \implies k = 600$.The equation is $2\sqrt{A} = -600t + 2000$.For bankruptcy,$A = 0$,so $0 = -600t + 2000$.$600t = 2000 \implies t = \frac{2000}{600} = \frac{20}{6} = \frac{10}{3}$ years.

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