The hominid fossil is 200 years old.
Determination of the number of half-lives
We'll begin by calculating the number of half-lives that has elapsed.
- Original amount (N₀) = 15424 g
- Amount remaining (N) = 14942 g
- Number of half-lives (n) =?
2ⁿ = N₀ / N
2ⁿ = 15424 / 14942
2ⁿ = 1.03
Take the log of both side
Log 2ⁿ = Log 1.03
nLog 2 = Log 1.03
Divide both side by Log 2
n = Log 1.03 / Log 2
n = 0.04
Determination of the age
Finally, we shall determine the age of the hominid fossil.
- Half-life (t½) = 5000 years
- Number of half-lives (n) = 0.04
t = n × t½
t = 0.04 × 5000
t = 200 years
Therefore, the hominid fossil is 200 years old.
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