Question

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
, 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

1
1

5
5

2

Answer 1

To determine a reasonable scale for the domain, we need to consider the width \( w \) of the fence. Since the total amount of fencing available is 40 yards, the width \( w \) must be between 0 and 20 yards (because if \( w \) were larger than 20, the length would become 0 or negative, which isn't possible for a garden).

A good approach is to choose a scale that allows you to calculate and observe the area \( A \) at various widths.

Here are the options you provided:

1. **10** - This scale would only allow for two values (0 and 10) in the domain, which would be insufficient to see the variation in area.

2. **1** - This gives a very fine scale with widths ranging from 0 to 20 in increments of 1 yard. It will provide a complete picture but may result in excessive values in your table.

3. **5** - This would allow for widths of 0, 5, 10, 15, and 20 yards, giving a good spread of values to calculate the areas without being overly detailed.

4. **2** - Similar to the 5 scale, but offers a little more granularity with values 0, 2, 4, 6, up to 20 yards.

Given these considerations, **5** yards is likely to be the most reasonable scale for the domain because it strikes a balance between usability and clarity of results. Thus, the best choice is **5**.