Answer:
t=160.82 years
Explanation:
exponential decay function is

If initial amount A_1 is 100 then material remaining is 99.57

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

take ln on both sides

k=-.00431

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

divide both sides by 100

take ln on both sides
t=160.82 years