1. **State the problem:** We have an element with an initial mass of 640 grams that decays by 7.3% per minute. We want to find how much of the element remains after 8 minutes, rounded to the nearest tenth of a gram. 2. **Formula used:** The decay can be modeled by exponential decay formula: $$m = m_0 \times (1 - r)^t$$ where: - $m$ is the remaining mass after time $t$ - $m_0$ is the initial mass - $r$ is the decay rate per time unit (as a decimal) - $t$ is the time elapsed 3. **Identify values:** - $m_0 = 640$ grams - $r = 7.3\% = 0.073$ - $t = 8$ minutes 4. **Calculate remaining mass:** $$m = 640 \times (1 - 0.073)^8$$ $$m = 640 \times (0.927)^8$$ 5. **Evaluate $(0.927)^8$:** $$0.927^8 \approx 0.5403$$ 6. **Multiply to find remaining mass:** $$m = 640 \times 0.5403 = 345.792$$ 7. **Round to nearest tenth:** $$m \approx 345.8 \text{ grams}$$ **Final answer:** After 8 minutes, approximately **345.8 grams** of the element remains.