Write the word or phrase that best completes each statement or answers the question.
-An artifact is discovered at a certain site. If it has $74 \%$ 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) $5920 \mathrm { yr }$
B) $2080 \mathrm { yr }$
C) $1046 \mathrm { yr }$
D) $2409 \mathrm { yr }$

Question

Quizplus · Accepted Answer

To find the age of the artifact, use the formula for exponential decay: $ N(t) = N_0 e^{-kt} $. Here, $ N(t)/N_0 = 0.74 $ and $ k = 0.000125 $. Solving $ 0.74 = e^{-0.000125t} $ gives $ t \approx 2409 $ years.

Write the Word or Phrase That Best Completes Each Statement 74%74 \%74%

Write the Word or Phrase That Best Completes Each Statement $74 \%$