Question

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

Answer 1

Help me answers this.

Answer 2

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