Question

A fossil fuel contains 70% of the carbon-14 it once had as a living creature. How would you use the half-life decay equation to determine when the creature died?

Answer 1

Let $N_0$ is initial amount of fossil fuel.

using half life equation,

$N=N_0\left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}}$

Let $\frac{t}{t_{1/2}}=n$

then, $N=N_0\left(\frac{1}{2}\right)^n$

a/c to question, fossil fuel contains 70% of the carbon-14.

so, $N=0.7N_0$

now, $0.7N_0=N_0\frac{1}{2^n}$

$0.7=2^{-n}$

taking log base 10 both sides,

$log(0.7)=-nlog2$

$0.155=nlog2$

$n=0.515$

it is experimentally that half life of carbon-14 = 5730 years

so, t/5730 = 0.515

or, t = 0.515 × 5730 = 2950 years