Question

A wooden artifact from an ancient tomb contains 30 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

N(t) = N0 * (1/2) ^ (t/h)

Where N(t) is the final amount
N0 is the initial amount
t is total time
and h is the half-life

Because it wants the point at which 30% of the sample is remaining, N(t) = 0.30 * N0 and therefore

0.30 * N0 = N0 * (1/2)^(t/h

The original amount N0 cancels out on both sides and you’re left with

0.30 = (1/2)^(t/h)
From there, you can plug in your half life h = 5730 and solve for t