If the half-life of an isotope $X$ is $10 \ yr$,its decay constant is (in $yr^{-1}$)

The half-life for radioactive decay of $^{14}C$ is $5730 \text{ years}$. An archaeological artifact containing wood had only $80\%$ of the $^{14}C$ found in a living tree. Which is the correct formula for age $(t)$ of the sample?

The half-life of radioactive $C^{14}$ is $5760 \ years$. In how many years will a $200 \ mg$ sample of $C^{14}$ be reduced to $25 \ mg$?

$A$ radioactive isotope has a half-life of $10 \, \text{years}$. What percentage of the original amount of it remains after $20 \, \text{years}$?

$A$ radioactive isotope decays at such a rate that after $192 \ min$ only $1/16$ of the original amount remains. The half-life of the radioactive isotope is ....... $\min$

$A$ sample is obtained from sea water. $11.9$ $C^{14}$ atoms dissociate from $1 \ g$ of carbon. $15.3$ $C^{14}$ atoms dissociate from a live sample. How many years old is the sample? $(t_{1/2} = 5730 \ \text{years})$