Analyzing a Dataset Quick Check

Question

1 of 51 of 5 Items
Question
Which of the following best models the data in the table?

Type of Function

The table presents values of x and y, showing how y increases as x increases
x y
2
8.5

4
46

6
107.5

8
193

(1 point)
Responses

cubic
cubic

quadratic
quadratic

linear
linear

exponential

Answer 1

To determine which type of function best models the data in the table, we can analyze how the value of \( y \) changes as \( x \) increases. We'll examine the differences in \( y \) values.

Given Data:

• For \( x = 2 \), \( y = 8.5 \)
• For \( x = 4 \), \( y = 46 \)
• For \( x = 6 \), \( y = 107.5 \)
• For \( x = 8 \), \( y = 193 \)

First Differences:

1. From \( 8.5 \) to \( 46 \): \( 46 - 8.5 = 37.5 \)
2. From \( 46 \) to \( 107.5 \): \( 107.5 - 46 = 61.5 \)
3. From \( 107.5 \) to \( 193 \): \( 193 - 107.5 = 85.5 \)

Differences:

• \( 37.5, 61.5, 85.5 \)

Second Differences:

1. From \( 37.5 \) to \( 61.5 \): \( 61.5 - 37.5 = 24 \)
2. From \( 61.5 \) to \( 85.5 \): \( 85.5 - 61.5 = 24 \)

Second Differences:

• \( 24, 24 \)

Since the second differences are constant, this indicates that the relationship between \( x \) and \( y \) can be best modeled by a quadratic function.

Conclusion:

The best model for the data in the table is quadratic.