# math

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An artifact was found and tested for its carbon-14 content. If 83% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? Use that carbon-14 has a half-life of 5,730 years.

• math -

x = Xo e^-kt
(x/Xo) = 1/2 = e^-(5730)k
ln .5 = -5730 k
-.693 =-5730 k

k = 1.21*10^-4

then

.83 = e^-1.21*10^-4 t

ln .83 = -1.21 * 10^-4 t = -.186
t = 10^4 * .154 = 1540 or 1500 years old

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