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?

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Answer 1 · 2016-01-30T03:18:35

The creature died 2950 yr ago.

The half-life equation is

$N = N_0(1/2)^(t/t_(1/2))$

Let $n = t/t_(1/2)$ . Then

$N = N_0(1/2)^n$ , or

$N/N_0 =1/2^n$

$N_0/N = 2^n$

$N_0/(0.70N_0) = 2^n$

$2^n = 1/0.70$

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

$n = 0.155/log2 = 0.515$

$t_(1/2) = "5730 yr"$ , and $n = t/t_(1/2)$ .

∴ $t = nt_(1/2) = "0.515 × 5730 yr" = "2950 yr"$