Radium decompose at the rate proportional to the amount present at any time. If $\mathrm{P} \%$ of amount…
Radium decompose at the rate proportional to the amount present at any time. If $\mathrm{P} \%$ of amount disappears in one year, then amount of radium left after 2 years is
$\left(10-\frac{P}{10}\right)^2$
$x_0\left[1+\frac{P}{100}\right]^2$
$x_0\left[1-\frac{P}{100}\right]^2$
$x_0\left[10-\frac{P}{100}\right]^2$
Solution
$\mathrm{P} \%$ amount disappears in one year.
Let initial amount of radium $=\mathrm{x}_0$
$\therefore$ Amount left after 1 year $=\mathrm{x}_0-\frac{\mathrm{P}}{100} \times \mathrm{x}_0=\mathrm{x}_0\left(1-\frac{\mathrm{P}}{100}\right)$
Amount left after 2 years
$\begin{aligned}
& =x_0\left(1-\frac{P}{100}\right)-\frac{P}{100} \times x_0\left(1-\frac{P}{100}\right) \\
& =x_0\left(1-\frac{P}{100}\right)\left(1-\frac{P}{100}\right)=x_0\left(1-\frac{P}{100}\right)^2
\end{aligned}$