A Radioactive Material with an Original Mass Of $10 \mathrm{~g}$ Has a Mass Of

Multiple Choice

A radioactive material with an original mass of $10 \mathrm{~g}$ has a mass of $8 \mathrm{~g}$ after 50 years. The material decays at a rate proportional to the amount present. Find an expression for the amount present at any time t. Also find its half-life.

A) $Q=10(0.8) ^{\frac{t}{50}}$ or $Q=10 e^{-0.004463 t}$ ; its half- life is about 155 years.
B) $\mathrm{Q}=10(0.8) ^{\frac{\mathrm{t}}{500}}$ or $\mathrm{Q}=10 \mathrm{e}^{-0.0004463 \mathrm{t}}$ ; its half- life is about 1553 years.
C) $\mathrm{Q}=10(8) ^{\frac{\mathrm{t}}{500}}$ or $\mathrm{Q}=10 \mathrm{e}^{0.004159 t}$ ; its half- life is about 167 years.
D) $\mathrm{Q}=8(0.1) ^{\frac{\mathrm{t}}{50}}$ or $\mathrm{Q}=8 \mathrm{e}^{-0.04605 \mathrm{t}}$ ; its half- life is about 15 years.