radioaxtive decay

Question

radioactive iodine decays according to the formula A(t)=A0×a^-t where A0 is the initial amount and t is time in days. find a, assuming the half life of radioactive iodine is 8 days. My route was: step 1) 1/2×A0 = A0×a^-t step 2) A0 cancels out step 3)1/2=a^-t. Step 4) Dont know where to go from here. The answer is a = 2^1/8 or about 1.09 How do I find this answer?

Answer 1

half-life=8 daes

yu did NOT sae the quesshun

normal tu wanna get time for it tu dekae til strong=x

OR wanna get nu strong after so much time go bi

idea be (now-strong)/(start-strong)=(1/2)^(how many half lifes go bi)

Sintifik tipes yuzeyually konvert it tu form:...(now/start)=e^-kt

weer t=how many daes or yeers or 100 milyun yeers (wotever relavent)

half-life meen now/start=1/2=0.5

take ln(e^-kt)=0.5 & yu get kt=ln(0.5)=0.693171805599453...rite side

ln(e^-kt)=-kt*ln(e)=-kt, so yu werk with kt=0.693171805599453

yu kan get a k that werk for daes or yeers or 100 milyun yeers