1. **State the problem:** We have an element with an initial mass of 420 grams that decays by 11.8% per minute. We want to find how much of the element remains after 16 minutes, rounded to the nearest tenth of a gram. 2. **Formula used:** The decay process follows exponential decay, modeled by the 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:** - $m_0 = 420$ grams - $r = 11.8\% = 0.118$ - $t = 16$ minutes 4. **Calculate remaining mass:** $$ m(16) = 420 \times (1 - 0.118)^{16} = 420 \times (0.882)^{16} $$ 5. **Evaluate the power:** Calculate $0.882^{16}$: $$ 0.882^{16} \approx 0.1033 $$ 6. **Multiply to find remaining mass:** $$ m(16) = 420 \times 0.1033 \approx 43.39 $$ 7. **Round to nearest tenth:** $$ 43.39 \approx 43.4 $$ grams **Final answer:** After 16 minutes, approximately **43.4 grams** of the element remain.