the amount 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 = ?(1 - )^

remaining amount = i(1 - r)^t

enter the number that belongs in the green box

Question

the amount 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 = ?(1 -  )^

remaining amount = i(1 - r)^t

enter the number that belongs in the green box

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 Growth Modeling" ], "new_concepts": [ "Exponential Decay Modeling" ], "current_concepts": [ "Exponential Growth Modeling", "Exponential Decay Modeling" ] } ## Identify the given values and formula Using the *Exponential Growth Modeling* knowledge point $$ \begin{aligned} &\text{Formula: } \text{Remaining Amount} = I(1 - r)^t \ &I = 50 \ &r = 50\% = 0.5 \ &\text{Interval: } 3 \text{ months} \ &t = \frac{12}{3} = 4 \end{aligned} $$ ## Match the green box value Using the *Exponential Growth Modeling* knowledge point $$ \begin{aligned} &\text{Remaining Amount} = 50(1 - 0.5)^4 \ &\text{Template: } [?](1 - \Box)^{\Box} \ &[?] = 50 \end{aligned} $$ Enter the number that belongs in the green box: 50 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Decay Modeling" ] }

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Question

Explanation:

Identify the given values and formula

Match the green box value

Answer: