Suppose a sample $of$ a certain substance decayed $to79\mathrm{.}8\%of$ its original amount after $300$ days.

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

$k=\frac{ln(0\mathrm{.}798)}{300}$

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

days

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

days