If 80% of a radioactive element remains radioactive after 250 years, what percent remains radioactive after 600 years? What is the half life of the element?
we use the formula $\displaystyle A(t) = A_0e^{-rt}$
where $\displaystyle A(t)$ is the amount remaining after time $\displaystyle t$, $\displaystyle A_0$ is the initial amount, and $\displaystyle r$ is the decay constant.
say $\displaystyle A_0 = 1$, then when $\displaystyle t = 250$, we have
$\displaystyle 0.8 = e^{-250r}$
use that equation to find $\displaystyle r$.
after that, you can answer the other questions (the half-life is easy, it is $\displaystyle \frac {\ln 2}r$)