An unknown radioactive element decays into non$-$radioactive substances. In $240$ days the radioactivity of a sample decreases by $74$ percent. Use the equation, $A(t)=A_o{e}^{kt}.$

$($a$)$ What is the half$-$life of the element?

half$-$life: $($days$)$

$($b$)$ How long will it take for a sample of $100$ mg to decay to $47$ mg $?$

time needer $($days$)$

Round to nearest hundredth.