Question

A wooden artifact from an ancient tomb contains 70% of the carbon-14 that is present in living trees. How long ago was the artifact made? (The half-life of carbon-14 is 5730 years. Round your answer to the nearest whole number.)

Answer 1

You know that every 5730 years, half of the carbon-14 decays. So the equation per year would be (1/2)^(x/5730). Now, to find 70 percent of the C-14 that has decayed, you would assign 100 as the original amount of carbon and 70 as the current amount. So...

Answer 2

70=100*(1/2)^(x/5730)

Answer 3

Now just solve for x

Answer 4

0.7=(1/2)^(x/5730)

Answer 5

log(base1/2)(0.7)=x/5730

Answer 6

x/5730 =log (base 10)(0.7)/ log(base 10) (0.5)=0.5146
so, x = 0.5146*5730=2948.5 or 2948 years