the half life of a certain substance is about 4 hours. the graph shows the decay of a 50 gram sample of the substance that is measured every hour for 9 hours.

which function can be used to determine the approximate number of grams of the sample remaining after $t$ hours?

$y = 25(0.15)^t$
$y = 25(0.85)^t$
$y = 50(0.15)^t$
$y = 50(0.85)^t$

Question

the half life of a certain substance is about 4 hours. the graph shows the decay of a 50 gram sample of the substance that is measured every hour for 9 hours.

which function can be used to determine the approximate number of grams of the sample remaining after $t$ hours?

$y = 25(0.15)^t$
$y = 25(0.85)^t$
$y = 50(0.15)^t$
$y = 50(0.85)^t$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Exponential Decay", "Half-Life Formula" ], "new_concepts": [], "current_concepts": [ "Exponential Decay", "Half-Life Formula", "Exponential Functions" ] } ## Identify the initial value Using the *Exponential Functions* knowledge point $$ a = 50 $$ ## Determine the decay factor Using the *Exponential Decay* and *Half-Life Formula* knowledge points $$ \begin{aligned} y &= a \cdot b^t \ y &= 50 \cdot (0.5)^{t/4} \ b &= (0.5)^{1/4} \approx 0.8409 \approx 0.85 \end{aligned} $$ ## Formulate the final function Using the *Exponential Functions* knowledge point $$ y = 50(0.85)^t $$

(A) $y = 25(0.15)^t$

(B) $y = 25(0.85)^t$

(C) $y = 50(0.15)^t$

(D) $y = 50(0.85)^t$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the initial value

Determine the decay factor

Formulate the final function

Answer: