# 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?

Jan 30, 2016

The creature died 2950 yr ago.

#### Explanation:

The half-life equation is

$N = {N}_{0} {\left(\frac{1}{2}\right)}^{\frac{t}{t} _ \left(\frac{1}{2}\right)}$

Let $n = \frac{t}{t} _ \left(\frac{1}{2}\right)$. Then

$N = {N}_{0} {\left(\frac{1}{2}\right)}^{n}$, or

$\frac{N}{N} _ 0 = \frac{1}{2} ^ n$

${N}_{0} / N = {2}^{n}$

${N}_{0} / \left(0.70 {N}_{0}\right) = {2}^{n}$

${2}^{n} = \frac{1}{0.70}$

nlog 2 = log 1 –log0.70 = 0 – (-0.155) = 0.155

$n = \frac{0.155}{\log} 2 = 0.515$

${t}_{\frac{1}{2}} = \text{5730 yr}$, and $n = \frac{t}{t} _ \left(\frac{1}{2}\right)$.

$t = n {t}_{\frac{1}{2}} = \text{0.515 × 5730 yr" = "2950 yr}$