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Note that the purpose of this task is algebraic in nature -- closely related tasks exist which approach similar problems from numerical or graphical stances.Now, take the logarithm of both sides to get $$ -0.693 = -5700k, $$ from which we can derive $$ k \approx 1.22 \cdot 10^{-4}.$$ So either the answer is that ridiculously big number (9.17e7) or 30,476 years, being calculated with the equation I provided and the first equation in your answer, respectively. When an organism dies, the amount of 12C present remains unchanged, but the 14C decays at a rate proportional to the amount present with a half-life of approximately 5700 years.This change in the amount of 14C relative to the amount of 12C makes it possible to estimate the time at which the organism lived.

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Carbon 14 is a common form of carbon which decays over time.

The amount of Carbon 14 contained in a preserved plant is modeled by the equation $$ f(t) = 10e^{-ct}.

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