A scientist measures the size in square inches of a fungus for several weeks after he administers an experimental fertilizer. The proportional relationship is shown in the table.

Question

Weeks 1
2
3
4
5

Total Size 214
412
634
9
1114


Which statement correctly describes the growth of the fungus in Week 3
and Week 4?

Select the answer that is completely correct.

Responses

The fungus grows 214
square inches from Week 3
to Week 4.
The size of the fungus is proportional to the week of measurement for any given week in the table, so it will grow by the same amount from Week 4
to Week 5.
The fungus grows 2 and 1 fourth square inches from Week 3 to Week The size of the fungus is proportional to the week of measurement for any given week in the table, so it will grow by the same amount from Week 4 to Week

The fungus grows 214
square inches from Week 3
to Week 4.
The size of the fungus is not proportional to the week of measurement for any given week in the table, so it will grow by a different amount from Week 4
to Week 5.
The fungus grows 2 and 1 fourth square inches from Week 3 to Week The size of the fungus is not proportional to the week of measurement for any given week in the table, so it will grow by a different amount from Week 4 to Week

The fungus grows 9
square inches from Week 3
to Week 4.
The size of the fungus is proportional to the week of measurement for any given week in the table, so it will grow by the same amount from Week 4
to Week 5.
The fungus grows 9 square inches from Week 3 to Week The size of the fungus is proportional to the week of measurement for any given week in the table, so it will grow by the same amount from Week 4 to Week

The fungus grows 9
square inches from Week 3
to Week 4.
The size of the fungus is not proportional to the week of measurement for any given week in the table, so it will grow by a different amount from Week 4
to Week 5.

Answer 1

To analyze the growth of the fungus from Week 3 to Week 4, we can look at the total size measurements from the table:

• Week 3: Total Size = 634 square inches
• Week 4: Total Size = 9 square inches (though this seems like a typographical error since sizes should be increasing, we will use this data to evaluate the options).

Let's determine how much the fungus grows from Week 3 to Week 4:

Growth from Week 3 to Week 4 = Size in Week 4 - Size in Week 3 = 9 - 634 = -625 square inches

This indicates that there is actually a decrease in size, suggesting an error in the data or its reporting. However, if we are solely interpreting the responses based on the statements provided:

1. The fungus does not grow positively from Week 3 to Week 4.
2. We cannot conclude it is proportional based on the erroneous data presented.

Now, looking at the provided options:

• The first and second options incorrectly claim growth of 214 and mention proportionality despite the negative growth.
• The third and fourth options incorrectly suggest a growth of 2 and 1/4 square inches, which is also incorrect.
• The fifth option incorrectly states growth of 9 square inches, and mentions proportional growth.
• The last option states the fungus grows 9 square inches and talks about lack of proportionality. However, 9 square inches is not an accurate value for growth.

Given these evaluations, it appears none of the statements are fully correct. The correct evaluation should indicate negative growth, which is not present among the statement choices provided.

But if we must select from the options provided:

The closest accurate option would be:

"The fungus grows 9 square inches from Week 3 to Week 4. The size of the fungus is not proportional to the week of measurement for any given week in the table, so it will grow by a different amount from Week 4 to Week 5."

While this option indicates a flaw in logic, as there is no growth of 9 square inches, it correctly captures the idea of non-proportional measurement if considering the table was misrepresented.

In a clear case, it's important to note that data should be reviewed for accuracy.