Half life algebra equation

Question

The model for radioactive decay is y=y0e^−kt. A radioactive substance has a half-life of 820 years. If 70 grams are present today, in how many years will 28 grams be present? While solving this problem, round the value of k to seven decimal places. Round your answer to two decimal places.

Answer 1

1/2=e^(-k820)

ln(1/2)=-820k

-ln2=-820k

k=ln2/820

28=70e^((-ln2/820)t)

.4=e^((-ln2/820)t)

ln.4=(-ln2/820)t

t=820ln.4/(-ln2)

t=1083.98