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{ "quality": "blurry", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Average Rate of Change" ], "new_concepts": [], "current_concepts": [ "Average Rate of Change", "Radical Functions" ] } ## Calculate the width values at the boundaries $$ \begin{aligned} W(289) &= \sqrt{289} = 17 \ W(400) &= \sqrt{400} = 20 \end{aligned} $$ ## Calculate the average rate of change $$ \begin{aligned} \text{Rate} &= \frac{W(400) - W(289)}{400 - 289} \ &= \frac{20 - 17}{111} \ &= \frac{3}{111} \ &\approx 0.027 \end{aligned} $$ ## Interpret the rate of change in context $$ \begin{aligned} \text{Rate} &\approx 0.027 \text{ feet per square foot} \end{aligned} $$

(A) The garden's width increases by approximately 18.50 feet for every 1 square foot increase in the garden's area.

(B) The garden's width increases by approximately 13.70 feet for every 1 square foot increase in the garden's area.

(C) The garden's width increases by approximately 0.027 feet for every 1 square foot increase in the garden's area.

(D) The garden's width increases by approximately 37.00 feet for every 1 square foot increase in the garden's area.

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

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Explanation:

Calculate the width values at the boundaries

Calculate the average rate of change

Interpret the rate of change in context

Answer: