1. **State the problem:** An element with an initial mass of 670 grams decays by 21.8% per minute. We want to find how much of the element remains after 15 minutes, rounded to the nearest tenth of a gram. 2. **Formula used:** The decay can be modeled by the exponential decay formula: $$ m(t) = m_0 \times (1 - r)^t $$ where: - $m(t)$ is the mass remaining after time $t$, - $m_0$ is the initial mass, - $r$ is the decay rate per unit time (as a decimal), - $t$ is the time elapsed. 3. **Identify values:** - $m_0 = 670$ grams - $r = 0.218$ (21.8% decay per minute) - $t = 15$ minutes 4. **Calculate remaining mass:** $$ m(15) = 670 \times (1 - 0.218)^{15} = 670 \times 0.782^{15} $$ 5. **Evaluate the power:** $$ 0.782^{15} \approx 0.0417 $$ 6. **Multiply to find remaining mass:** $$ m(15) = 670 \times 0.0417 = 27.939 $$ 7. **Round to nearest tenth:** $$ 27.939 \approx 27.9 $$ grams **Final answer:** After 15 minutes, approximately **27.9 grams** of the element remain.