Answer:
t=160.82 years
Step-by-step explanation:
exponential decay function is
[tex]A= A_1 e^{kt}[/tex]
If initial amount A_1 is 100 then material remaining is 99.57
[tex]99.57=100e^{kt}[/tex]
divide both sides by 100, question says 1 year so t=1
[tex].9957=e^{k(1)}[/tex]
take ln on both sides
[tex]ln(.9957)=k[/tex]
k=-.00431
[tex]A=100e^{-.00431t}[/tex]
t=1, A= 50 remaining (half life)
[tex]50=100e^{-.00431(t)}[/tex]
divide both sides by 100
[tex]0.5=e^{-.00431t}[/tex]
take ln on both sides
t=160.82 years
