find the table of values which has lesser rate of change.

Question

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": [ "Rate of Change Comparison" ], "new_concepts": [], "current_concepts": [ "Rate of Change Comparison", "Average Rate of Change" ] } ## Calculate average rate of change for the first table Using the **Rate of Change Comparison** knowledge point $$ \begin{aligned} &\text{Interval: } [1, 3]\ &m_1 = \frac{y(3) - y(1)}{3 - 1} = \frac{3 - 4}{3 - 1} = -\frac{1}{2} = -0.5 \end{aligned} $$ ## Calculate average rate of change for the second table Using the **Rate of Change Comparison** knowledge point $$ \begin{aligned} &\text{Interval: } [0, 4]\ &m_2 = \frac{y(4) - y(0)}{4 - 0} = \frac{10 - 6}{4 - 0} = \frac{4}{4} = 1 \end{aligned} $$ ## Compare the rates of change Using the **Rate of Change Comparison** knowledge point $$ \begin{aligned} &-0.5 < 1 \implies m_1 < m_2 \end{aligned} $$

(A) The table with values: x = [1, 2, 3], y = [4, 5, 3]

(B) The table with values: x = [0, 3, 4], y = [6, 15, 10]

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Rate of Change Comparison" ] }

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Question

Explanation:

Calculate average rate of change for the first table

Calculate average rate of change for the second table

Compare the rates of change

Answer: