$A$ radioactive element has a half-life of $1 \text{ day}$. After $3 \text{ days}$,the amount of the element left will be:

$A$ radioactive isotope has a half-life of $10 \ days$. If today $125 \ mg$ is left over,what was its original weight $40 \ days$ earlier?

$A$ radioactive substance has a half-life $(t_{1/2})$ of $60 \ minutes$. After $3 \ hours$,what percentage of the radioactive substance will remain?

$A$ wood specimen from an archeological site shows a $_6^{14}C$ activity of $5.0 \ counts/min/gm$ of carbon. If a freshly cut wood gives $15 \ counts/min/gm$ of carbon,what is the age of the specimen? (Given: $t_{1/2}$ for $_6^{14}C$ is $5000 \ years$)

$^{18}_{8}O$ has a half-life of $4650 \text{ years}$. $200 \text{ mg}$ of a sample of $^{18}_{8}O$ is reduced to $25 \text{ mg}$ in ......... $\text{years}$.

If $n_t$ number of radioatoms are present at time $t$,the following expression will be a constant: