Algebra equation question

Question

The radioactive element​ carbon-14 has a​ half-life of 5750 years. A scientist determined that the bones from a mastodon had lost

53.7​%

of their​ carbon-14. How old were the bones at the time they were​ discovered?

Answer 1

50% is lost in 5,760 years

53% is lost in maybe a little longer, such as over 6,000 years

1/2 = e^rt = e^5760r

take natural logs of both sides

ln.5 = 5760r, divide by 5760

r = ln.5/5760 = -..0001228 decay rate

if it lost 53.7%, then 46.3% remains

.463 = e^-.00012034t

ln.463 = -.00012034t

t = ln.463/-.00012034 = 6399 years old or about 6400 years