A Radioactive Isotope Is Released into the Air as an Industrial

Multiple Choice

A radioactive isotope is released into the air as an industrial by-product.This isotope is not very stable due to radioactive decay.Two-thirds of the original radioactive material loses its radioactivity after each month.If 12 grams of this isotope are released into the atmosphere at the end of the first and every subsequent month, identify the closed form sum that gives the amount of the isotope in the atmosphere at the end of the n^th month.

A) $S_{n}=\frac{12-\left(\frac{1}{3}\right) ^{n} \cdot 12}{1-\frac{1}{3}}$
B) $S_{n}=\frac{12+\left(\frac{1}{3}\right) ^{n} \cdot 12}{\frac{1}{3}}$
C) $S_{n}=\frac{12 \cdot\left(\frac{1}{3}\right) ^{n}}{1-\frac{1}{3}}$