Acertain radioactive isotope has leaked into a small stream. four
hundred days after the leak, 13% of the original amount of the substance remained. determine the half-life of this radioactive isotope.

Ok so

for a thing that is P amount at first, with a half life of k days
after t days, the amount left is A

the equation is


given
13% of P remained=A
t=400

replace A with 0.13P and t with 400

0.13P=
divide both sides by P

take the ln of both sides

multiply both sides by k

divide oth sides by ln0.13
k=
evaluate
k=135.897 days

the half life is 135.897 days