Pre-Calculus. .

Question

The radioactive element​ carbon-14 has a​ half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 59.7% of their​ carbon-14. How old were the bones at the time they were​ discovered?

Answer 1

The general form of the decay equation is S = S_oe-kt

where

S = amount remaining, S_o = the initial amount, k = decay constant, & t = time in years

Then to find k: (assume we start with 100 lbs as the intial amount & have half left)

50 = 100e^-k(5750) or 1/2 = e^-k(5750) Solving for k = .00012055

To find the age of the bones, assume we start with 100 lbs of bones

Then

59.7 = 100e^{-(.00012055)t} Solving for t = 4,279 years