1. **State the problem:** We want to find how much of a radioactive substance remains after 12 months if its half-life is 3 months and the initial amount is 50 grams. 2. **Formula used:** The amount remaining after time $t$ can be calculated using the half-life formula: $$ A = A_0 \left(\frac{1}{2}\right)^{\frac{t}{T}} $$ where: - $A$ is the amount remaining, - $A_0$ is the initial amount, - $t$ is the elapsed time, - $T$ is the half-life. 3. **Apply the values:** Here, $A_0 = 50$ grams, $t = 12$ months, and $T = 3$ months. 4. **Calculate the exponent:** $$ \frac{t}{T} = \frac{12}{3} = 4 $$ 5. **Calculate the remaining amount:** $$ A = 50 \times \left(\frac{1}{2}\right)^4 = 50 \times \frac{1}{16} = 3.125 $$ 6. **Interpretation:** After 12 months, 3.125 grams of the substance will remain. **Final answer:** $$ \boxed{3.125 \text{ grams}} $$