Choose the one alternative that best completes the statement or answers the question.
-An artifact is discovered at a certain site. If it has $65 \%$ of the carbon-14 it originally contained, what is the approximate age of the artifact to the nearest year? (carbon-14 decays at the rate of $0.0125 \%$ annually.)
A) $5200 \mathrm { yr }$
B) $1497 \mathrm { yr }$
C) $2800 \mathrm { yr }$
D) $3446 \mathrm { yr }$

Question

Quizplus · Accepted Answer

The decay rate of carbon-14 is $0.0125\%$ annually. Using the formula for exponential decay, $N(t) = N_0 e^{-kt}$, where $N(t)$ is the remaining amount, $N_0$ is the initial amount, $k$ is the decay constant, and $t$ is time, we can solve for $t$. Given $N(t)/N_0 = 0.65$ and $k = 0.000125$, solving $0.65 = e^{-0.000125t}$ gives $t \approx 3446$ years.

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