Give the equation form of the exponential law of radioactive decay.

$x$ fraction of a radioactive sample decays in $t$ time. What fraction will decay in $2t$ time?

The activity of an element becomes $\frac{1}{64}$ of its original value in $60 \ s$. Then the half-life period is ............ $s$.

$A$ radioactive material decays by simultaneous emission of two particles with respective half-lives $1620$ years and $810$ years. The time (in years) after which one-fourth of the material remains is:

Half-life of a radioactive element is $10 \, days$. The time during which the quantity remains $1/10$ of the initial mass will be ......... $days$.

The relation between the mean life time $\tau$ and the half-life time $T_{1/2}$ of a radioactive substance is: