College Algebra 1314

Question

The radioactive element carbon-14 has half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 57.8% of their carbon-14. How old were the bones at the time they were discovered?

Answer 1

1/2 = e^5750r

50% is left after 5750 years

57% left after a little shorter time period, maybe 5000 years old give or take 500 years

1/2 = e^(rt) = e^5750r where t= years, and r= rate of growth

ln(1/2) = 5750r

r = ln(1/2)/5750 = -.693/5750 = -1.2055x10^-4

A = Pe^(-1.2055x10^-4)t

.57 = e(-1.2055x10^-4)t4

ln.57 = -1.2055x10^-4)t

t = ln.57/-1.2055x10^-4 = about 4663 years old bones