Question

If 60​% of a radioactive element remains radioactive after 200 million​ years, then what percent remains radioactive after 500 million​ years?

Answer 1

m = M e^-kt
m/M = 0.60 = e^-k(200)
ln 0.60 = -200 k
-.511 = -200 k
k = 0.00170/million years

m/M = e^-0.00170(500)
= 0 .427
so
42.7 %

for half life
0.5 = e^-.00170 t
ln .5 = -.0017 t
solve for t in millions of years

Answer 2

Once you do that, you realize it is reasonable, as at 200 million years, it has not reached the first half life yet, and at 500 million years, it has, and not quite half is left.
Good work, Lola. Thanks.