If the amount of a sample of radioactive substance that remains after t years is given by $Q ( t ) = Q _ { 0 } e ^ { - 0.0003 t }$ and 500 grams of the substance remain at the end of 7,000 years, then there were about 4,083 grams present initially.

Question

Quizplus · Accepted Answer

To find the initial amount $Q_0$, we use the formula $Q(t) = Q_0 e^{-0.0003 \times 7000}$. Given $Q(7000) = 500$, we solve for $Q_0$: $500 = Q_0 e^{-2.1}$. Solving this gives $Q_0 \approx 4083$ grams.

If the Amount of a Sample of Radioactive Substance That Q(t)=Q0e−0.0003tQ ( t ) = Q _ { 0 } e ^ { - 0.0003 t }Q(t)=Q0​e−0.0003t

If the Amount of a Sample of Radioactive Substance That $Q ( t ) = Q _ { 0 } e ^ { - 0.0003 t }$