The rate of reduction of a person's assets is | vedclass

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(C) Let $A$ be the assets at time $t$. The rate of reduction is given by $\frac{dA}{dt} = -k\sqrt{A}$, where $k > 0$.Separating variables: $\frac{dA}{

Vedclass · Accepted Answer

$8$

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(C) Let $A$ be the assets at time $t$. The rate of reduction is given by $\frac{dA}{dt} = -k\sqrt{A}$, where $k > 0$.Separating variables: $\frac{dA}{\sqrt{A}} = -k dt$.Integrating both sides: $2\sqrt{A} = -kt + C$.At $t = 0$, $A = 10000$, so $2\sqrt{10000} = C \implies C = 200$.Thus, $2\sqrt{A} = 200 - kt$.At $t = 2$, $A = 5625$, so $2\sqrt{5625} = 200 - 2k \implies 2(75) = 200 - 2k \implies 150 = 200 - 2k \implies 2k = 50 \implies k = 25$.The equation is $2\sqrt{A} = 200 - 25t$.For bankruptcy, $A = 0$, so $0 = 200 - 25t \implies 25t = 200 \implies t = 8$ years.

The rate of reduction of a person's assets is proportional to the square root of their existing assets at that moment. If the assets at the beginning are $10000$ and they dwindle down to $5625$ in $2$ years, then the person will be bankrupt in: (in $years$)

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