A sample contains 75 grams of carbon $\left( { } ^ { 14 } C \right) . { } ^ { 14 } C$ has a half-life of 5715 years. How much ${ } ^ { 14 } \mathrm { C }$ remains after 100 years? Round your answer to three decimal places.
A) $73.688$ grams
B) $74.096$ grams
C) $49.524$ grams
D) $1.312$ grams
E) $37.524$ grams

Question

Quizplus · Accepted Answer

The decay formula is $ N(t) = N_0 \times (1/2)^{t/T} $, where $ N_0 = 75 $ grams, $ t = 100 $ years, and $ T = 5715 $ years. Plugging in the values, $ N(100) = 75 \times (1/2)^{100/5715} \approx 74.096 $ grams.

A Sample Contains 75 Grams of Carbon (14C).14C\left( { } ^ { 14 } C \right) . { } ^ { 14 } C(14C).14C

A Sample Contains 75 Grams of Carbon $\left( { } ^ { 14 } C \right) . { } ^ { 14 } C$