Elena knows that Lea has a garden with an area of 100 square meters. She does not know the specific width, $w$, and length, $l$ of the garden.

The graph below represents the widths that correspond to possible lengths of Lea's garden.

As the possible width of Lea's garden increases, what does its possible length approach?
Choose 1 answer:
(A) $\infty$
(B) 0
(C) 10
(D) $\mathbf{1 2 0}$

Question

Elena knows that Lea has a garden with an area of 100 square meters. She does not know the specific width, $w$, and length, $l$ of the garden.

The graph below represents the widths that correspond to possible lengths of Lea's garden.

As the possible width of Lea's garden increases, what does its possible length approach?
Choose 1 answer:
(A) $\infty$
(B) 0
(C) 10
(D) $\mathbf{1 2 0}$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To determine the behavior of the length $l$ as the width $w$ increases, we need to analyze the graph's trend. ‖ ‖ step 2 ⋮ The graph shows that as $w$ increases, the curve approaches a horizontal line near the y-axis value of 10. ‖ ‖ step 3 ⋮ This suggests that the length $l$ approaches a value close to 10 as the width $w$ becomes larger. ‖ ‖ step 4 ⋮ Since the area of the garden is 100 square meters, the relationship between the width $w$ and length $l$ must satisfy the equation $w \cdot l = 100$. ‖ ‖ step 5 ⋮ As $w$ increases, $l$ must decrease to maintain the constant area of 100 square meters, but the graph indicates that $l$ does not decrease to 0. ‖ ∻[question number] Answer∻ ***C*** ∻Key Concept∻ ⚹Asymptotic Behavior⚹ ∻Explanation∻ ⚹The length $l$ approaches a horizontal asymptote as the width $w$ increases, indicating that $l$ approaches a constant value.⚹◊What is the equation of the cosine function graphed in the interactive widget?⍭ Generate me a similar question◊

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