Solution Given: Half-life t1/2=2t_{1/2}=2t1/2=2 years Q0=200Q_0=200Q0=200 grams Q(t)=Q0(12)t/2Q(t)=Q_0\left(\frac{1}{2}\right)^{t/2}Q(t)=Q0(21)t/2 We need Q(6)Q(6)Q(6): Q(6)=200(12)6/2=200(12)3=200⋅18=25\begin{aligned} Q(6)&=200\left(\frac{1}{2}\right)^{6/2}\\ &=200\left(\frac{1}{2}\right)^3\\ &=200\cdot\frac{1}{8}\\ &=25 \end{aligned}Q(6)=200(21)6/2=200(21)3=200⋅81=25 Q(6)=25 grams\boxed{Q(6)=25\ \text{grams}}Q(6)=25 grams Graphically, this matches the fact that every 2 years the quantity halves: 200→100→50→25(after 6 years)200\to 100\to 50\to 25\quad \text{(after 6 years)}200→100→50→25(after 6 years)