Marilee is creating a garden in her yard. She needs to put up a fence to keep the animals out of it. She has 40 yards of fencing she can erect. This situation is modeled using the equation A=−w2+20w

Question

, where A
is the area of the fence and w is the width of the fence. If you were to set up a table to determine the measurements of the width and its corresponding area, what would be a reasonable scale for the domain?(1 point)
Responses

10
10

2
2

5
5

1

Answer 1

To determine a reasonable scale for the domain of the width \( w \) in the equation \( A = -w^2 + 20w \), we need to consider the constraints of the situation. The maximum width of the garden's fence can be derived from the given total fencing of 40 yards, which can be expressed in terms of width (\( w \)) and length (\( l \)) using the perimeter formula for a rectangular area, given by \( P = 2l + 2w = 40 \).

Since the maximum \( w \) value occurs when the length is minimized (approaching zero), we find that \( w \) can range from 0 to a value close to 20 yards (which is \( w = 20 \) when \( l = 0 \)). Thus, you would likely choose a scale that allows you to examine different values of width within this interval.

Therefore, a reasonable scale for the domain of \( w \) would be 2 or 5. However, among the given options, the best choice for a reasonable scale for the width \( w \) in practical terms would be 2, as it allows for easier calculations and more detailed insights into the unit intervals covered in the range from 0 to 20.

So the answer is:

2