1. **Problem Statement:** We are given a radioactive substance with a half-life of 1 week. Starting with 70 grams, we want to find how much remains after 3 weeks. 2. **Formula:** The amount remaining after time $t$ is given by $$A = A_0 \left(\frac{1}{2}\right)^{\frac{t}{T}}$$ where: - $A_0$ is the initial amount, - $T$ is the half-life, - $t$ is the elapsed time. 3. **Given values:** - $A_0 = 70$ grams - $T = 1$ week - $t = 3$ weeks 4. **Calculation:** Substitute the values into the formula: $$A = 70 \left(\frac{1}{2}\right)^{\frac{3}{1}} = 70 \left(\frac{1}{2}\right)^3$$ 5. **Simplify:** $$\left(\frac{1}{2}\right)^3 = \frac{1}{2^3} = \frac{1}{8}$$ 6. **Final amount:** $$A = 70 \times \frac{1}{8} = 8.75$$ grams **Answer:** After 3 weeks, 8.75 grams of the substance remain.