In September 1987, Goiânia was the site of the largest radioactive accident that occurred in Brazil, when a sample of caesium-137, removed from an abandoned radiotherapy device, was inadvertently handled by part of the population. The half-life of a radioactive material is the time required for the mass of that material to be reduced to half. The half-life of caesium-137 is 30 years and the amount of remaining mass of a radioactive material, after $t$ years, is calculated by the expression $M(t) = A \cdot (2.7)^{kt}$, where $A$ is the initial mass and $k$ is a negative constant. Consider 0.3 as an approximation for $\log_{10} 2$. What is the time required, in years, for an amount of caesium-137 mass to be reduced to 10\% of the initial amount? (A) 27 (B) 36 (C) 50 (D) 54 (E) 100
In September 1987, Goiânia was the site of the largest radioactive accident that occurred in Brazil, when a sample of caesium-137, removed from an abandoned radiotherapy device, was inadvertently handled by part of the population. The half-life of a radioactive material is the time required for the mass of that material to be reduced to half. The half-life of caesium-137 is 30 years and the amount of remaining mass of a radioactive material, after $t$ years, is calculated by the expression $M(t) = A \cdot (2.7)^{kt}$, where $A$ is the initial mass and $k$ is a negative constant.
Consider 0.3 as an approximation for $\log_{10} 2$.
What is the time required, in years, for an amount of caesium-137 mass to be reduced to 10\% of the initial amount?
(A) 27
(B) 36
(C) 50
(D) 54
(E) 100