Question

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

Explanation:

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"concepts_used": [
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"current_concepts": [
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"Average Rate of Change"
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<reasoning>

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
\[

$$\begin{aligned} &-0.5 < 1 \implies m_1 < m_2 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) The table with values: x = [1, 2, 3], y = [4, 5, 3]</mcq-correct>
<mcq-option>(B) The table with values: x = [0, 3, 4], y = [6, 15, 10]</mcq-option>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
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]
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</post_analysis>

Answer:

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</pre_analysis>

<reasoning>

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
\[

$$\begin{aligned} &-0.5 < 1 \implies m_1 < m_2 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) The table with values: x = [1, 2, 3], y = [4, 5, 3]</mcq-correct>
<mcq-option>(B) The table with values: x = [0, 3, 4], y = [6, 15, 10]</mcq-option>
</answer>

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