The age of the bone is 45840 years.
We'll begin by calculating the number of half-lives that has elapsed.
Amount remaining (N) = 0.3125 g
Initial amount (N₀) = 80 g
Number of half-lives (n) =?
N × 2ⁿ = N₀
0.3125 × 2ⁿ = 80
Divide both side by 0.3125
2ⁿ = 80 / 0.3125
2ⁿ = 256
2ⁿ = 2⁸
n = 8
Thus, 8 half-lives has elapsed
Finally, we shall determine the age of the bone.
Half-life (t½) = 5730 years
Number of half-lives (n) = 8
Time (t) =?
t = n × t½
t = 8 × 5730
t = 45840 years
Therefore, the age of the bone is 45840 years.
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