Radium decomposes at a rate proportional to t | vedclass

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(C) Let the initial amount of radium be $x_0$. Since the rate of decomposition is proportional to the amount present,the amount remaining follows an e

Vedclass · Accepted Answer

$x_0\left[1-\frac{P}{100}\right]^2$

Vedclass · Answer

(C) Let the initial amount of radium be $x_0$. Since the rate of decomposition is proportional to the amount present,the amount remaining follows an exponential decay model. After $1$ year,$P \%$ of the amount disappears,so the amount remaining is $x_1 = x_0 - \frac{P}{100}x_0 = x_0\left(1-\frac{P}{100}ight)$. Let $k = \left(1-\frac{P}{100}ight)$ be the fraction remaining after each year. After $2$ years,the amount remaining is $x_2 = x_1 	imes k = x_0\left(1-\frac{P}{100}ight) 	imes \left(1-\frac{P}{100}ight) = x_0\left(1-\frac{P}{100}ight)^2$.

Radium decomposes at a rate proportional to the amount present at any time. If $P \%$ of the amount disappears in one year,then the amount of radium left after $2$ years is

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