1. **State the problem:** We have an element with an initial mass of 450 grams that decays by 19.4% per minute. We want to find how much of the element remains after 17 minutes, rounded to the nearest tenth of a gram. 2. **Formula for exponential decay:** The amount remaining after time $t$ is given by: $$ A = A_0 \times (1 - r)^t $$ where: - $A_0$ is the initial amount (450 grams), - $r$ is the decay rate per time unit (19.4% = 0.194), - $t$ is the time elapsed (17 minutes). 3. **Calculate the remaining amount:** $$ A = 450 \times (1 - 0.194)^{17} = 450 \times (0.806)^{17} $$ 4. **Evaluate the power:** Calculate $(0.806)^{17}$: $$ (0.806)^{17} \approx 0.0413 $$ 5. **Multiply by initial amount:** $$ A = 450 \times 0.0413 = 18.585 $$ 6. **Round to nearest tenth:** $$ A \approx 18.6 \text{ grams} $$ **Final answer:** After 17 minutes, approximately **18.6 grams** of the element remain.