Suppose a sample of a certain substance decayed to $65\mathrm{.}2\%$ of its original amount after $300$ days.

Let $y(t)=A{e}^{kt}$ be the mass remaining after $t$ days. Find the exact value of $k.$

k $=$

What is the half$-$life $($in days$)$ of this substance? $($Round your answer to two decimal places.$)$

$$ days

How long woutd it take the sample to decay to one$-$third of its original amount? $($Round your answer to two decimal places.$)$

$$ days