Question

Radioactive Decay

Answer 1

Answer:

t=160.82 years

Step-by-step explanation:

exponential decay function is

$A= A_1 e^{kt}$

If initial amount A_1 is 100 then material remaining is 99.57

$99.57=100e^{kt}$

divide both sides by 100, question says 1 year so t=1

$.9957=e^{k(1)}$

take ln on both sides

$ln(.9957)=k$

k=-.00431  

$A=100e^{-.00431t}$

t=1, A= 50 remaining (half life)

$50=100e^{-.00431(t)}$

divide both sides by 100

$0.5=e^{-.00431t}$

take ln on both sides

t=160.82 years