A synthetic radioisotope used in targeted radiotherapy decays via first-order kinetics with a rate constant \(k = 2.77 \times 10^{-2} \text{ day}^{-1}\). A hospital laboratory receives a sealed container holding a \(32.0 \text{ mg}\) sample of this pure isotope. Assuming no additional isotope is introduced, which of the following is the mass of the radioisotope remaining in the container after \(100 \text{ days}\)?