A geologist is studying a radioactive sample he has recently collected. The initial weight of the sample is $18.61 \mathrm{~g}$. When each atom emits its $\alpha$-particle, the mass of the atom is reduced by $2.2 \%$. The mass of the sample is given by $M(t)=A+B\left(\frac{1}{2}\right) \frac{t}{20 s}, t \geqslant 0$ days. a Explain why $A$ is the final mass of the sample after every atom in the sample has emitted its $\alpha$-particle, and find its value. $[2]$ b Find the value of $B$. c Estimate the mass of the sample after 2 years. [2] [2]

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