the mass of a particular radioactive substance decreases by 50% every 3 months. if you started with 50 grams of this substance, how much of it would remain after 12 months?

remaining amount = $50(1 - 0.50)^4$

remaining amount = ? grams

round your answer to the nearest whole number.

Question

the mass of a particular radioactive substance decreases by 50% every 3 months. if you started with 50 grams of this substance, how much of it would remain after 12 months?

remaining amount = $50(1 - 0.50)^4$

remaining amount =  ?  grams

round your answer to the nearest whole number.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Exponential Decay Modeling" ], "new_concepts": [ "Half-Life Calculations" ], "current_concepts": [ "Exponential Decay Modeling", "Half-Life Calculations" ] } ## Identify the given values and formula Using the *Exponential Decay Modeling* knowledge point $$ \begin{aligned} &A_0 = 50\ &r = 0.50\ &n = \frac{12}{3} = 4\ &A = 50(1 - 0.50)^4 \end{aligned} $$ ## Calculate the remaining amount Using the *Exponential Decay Modeling* knowledge point $$ \begin{aligned} &A = 50(0.50)^4\ &A = 50(0.0625)\ &A = 3.125 \end{aligned} $$ ## Round to the nearest whole number Using the *Exponential Decay Modeling* knowledge point $$ \begin{aligned} &A \approx 3 \end{aligned} $$ Remaining Amount = 3 grams { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Decay Modeling" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given values and formula

Calculate the remaining amount

Round to the nearest whole number

Answer: