an element with mass 870 grams decays by 25.9% per minute. how much of the element is remaining after 20 minutes, to the nearest 10th of a gram?

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Exponential Decay" ], "current_concepts": [ "Exponential Decay", "Exponential Growth" ] } ## Set up the exponential decay formula $$ \begin{aligned} &A = P(1 - r)^t \ &P = 870 \ &r = 0.259 \ &t = 20 \end{aligned} $$ ## Calculate the remaining mass $$ \begin{aligned} &A = 870(1 - 0.259)^{20} \ &A = 870(0.741)^{20} \ &A \approx 870 \times 0.0024467 \ &A \approx 2.1286 \end{aligned} $$ ## Round to the nearest tenth of a gram $$ A \approx 2.1\text{ grams} $$ $2.1$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Decay" ] }

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Explanation:

Set up the exponential decay formula

Calculate the remaining mass

Round to the nearest tenth of a gram

Answer: