How long ago, to the nearest year, was the artifact made?

Question

A wooden artifact from an ancient tomb contains 35 percent of the carbon-14 that is present in living trees. How long ago, to the nearest year, was the artifact made? (The half-life of carbon-14 is 5730 years.)

Answer 1

Hello, Xochitl,

There are several equations that can be used for this calculation. Please find the one you are studying, and perhaps post it.

The equation I will use is:

N(t) = N(0)e^-0.0001216t

N(t) and N(0) are the final and initial radioactive material. The -0.00012 is a constant for carbon-14 decay, and t is the years.

We can state:

0.35 = 1.00e^-0.0001216t and solve for t by taking the natural log of both sides:

ln(0.35) = -0.0001216t

-1.0498221 = -0.0001216t

t = 8633 years

Bob