Use the table to answer the question.

Question

l
A(l)
2 8
4 16
6 24
8 32
Kalani is trying to decide how large she wants the total area of her garden to be. The table shows some of the possibilities she is considering for the length of one side (l)
and the total area of the garden, A(l)
. Which of the following equations describes the relationship between side length and area, as outlined in this table, using function notation?

(1 point)
Responses

A(l)=2l
upper A left parenthesis l right parenthesis equals 2 l

A(l)=4l
upper A left parenthesis l right parenthesis equals 4 l

A(w)=l+4
upper A left parenthesis w right parenthesis equals l plus 4

A(w)=l+2
upper A left parenthesis w right parenthesis equals l plus 2
Remaining Attempts : 3
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Answer 1

To determine the correct equation that describes the relationship between the length of one side \( l \) and the total area \( A(l) \) as given in the table, we can examine the data:

\[ \begin{align*} l & : A(l) \ 2 & : 8 \ 4 & : 16 \ 6 & : 24 \ 8 & : 32 \ \end{align*} \]

Looking for a pattern, we can see that:

• When \( l = 2 \), \( A(2) = 8 \)
• When \( l = 4 \), \( A(4) = 16 \)
• When \( l = 6 \), \( A(6) = 24 \)
• When \( l = 8 \), \( A(8) = 32 \)

We notice that \( A(l) \) is 4 times the value of \( l \) at each point:

\[ A(2) = 4 \times 2 = 8 \ A(4) = 4 \times 4 = 16 \ A(6) = 4 \times 6 = 24 \ A(8) = 4 \times 8 = 32 \]

Thus, the relationship between area and length is \( A(l) = 4l \).

So, the correct answer is:

A(l) = 4l