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Mathematics
Jade2cool4u:

An archaeologist and turkey discovers a spear head that contains 32% of its original amount of C-14

Jade2cool4u:

Help me answers this.

Mercury:

next time please post the whole question (it is asking about the age of the spearhead) the decay formula is \[N(t) = N_{0}e^{kt}\] where N(t) is the final amount, N_0 is the initial amount, k is the decay constant, and t is time we need to find k first. let's start at exactly 1 half life passed (5730 years, this is the known half-life of C-14). at one half life, N(t) = 1/2(N_0) plugging things in 1/2(N_0) = N_0 e^(k*5730) solve for k from there, go back to the original equation \[N(t) = N_{0}e^{kt}\] plug in k, let N(t) = 32% of N_0, solve for t

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