allie claims that this data represents a nonlinear relation that is also quadratic. is she correct?

yes
no

Question

allie claims that this data represents a nonlinear relation that is also quadratic. is she correct?

yes
no

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": [ "First Differences", "Second Differences", "Quadratic Relations" ], "new_concepts": [ "Exponential Relations" ], "current_concepts": [ "First Differences", "Second Differences", "Quadratic Relations", "Exponential Relations" ] } ## Calculate first differences Using the *First Differences* knowledge point $$ \begin{aligned} &d_1 = 500 - 250 = 250 \ &d_2 = 1000 - 500 = 500 \ &d_3 = 2000 - 1000 = 1000 \ &d_4 = 4000 - 2000 = 2000 \ &d_5 = 8000 - 4000 = 4000 \ &d_6 = 16000 - 8000 = 8000 \end{aligned} $$ ## Calculate second differences Using the *Second Differences* knowledge point $$ \begin{aligned} &s_1 = 500 - 250 = 250 \ &s_2 = 1000 - 500 = 500 \ &s_3 = 2000 - 1000 = 1000 \ &s_4 = 4000 - 2000 = 2000 \ &s_5 = 8000 - 4000 = 4000 \end{aligned} $$ ## Analyze relation type Using the *Quadratic Relations* knowledge point $$ \begin{aligned} &\text{First differences are not constant} \implies \text{Nonlinear} \ &\text{Second differences are not constant} \implies \text{Not Quadratic} \ &\text{Ratio of consecutive terms is constant: } \frac{500}{250} = \frac{1000}{500} = 2 \implies \text{Exponential} \end{aligned} $$

yes

no

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Relations" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate first differences

Calculate second differences

Analyze relation type

Answer: