Which type of function best models the data in the table?

Question

Time and Growth Data

Time (days) Growth (inches)
1
1
0
0

3
3
12
12

5
5
32
32

7
7
60
60

(1 point)
Responses

exponential
exponential

cubic
cubic

linear
linear

quadratic

Answer 1

To determine which type of function best models the given growth data, we need to analyze the growth values in relation to time.

Here is the data summarized:

• At 1 day, growth = 0
• At 3 days, growth = 12
• At 5 days, growth = 32
• At 7 days, growth = 60

We can calculate the differences in growth to see if they fit any specific pattern:

First Differences:

• Growth at 3 days - Growth at 1 day = 12 - 0 = 12
• Growth at 5 days - Growth at 3 days = 32 - 12 = 20
• Growth at 7 days - Growth at 5 days = 60 - 32 = 28

First differences:

• From 0 to 12: 12
• From 12 to 32: 20
• From 32 to 60: 28

Second Differences:

• Difference between 20 and 12 = 20 - 12 = 8
• Difference between 28 and 20 = 28 - 20 = 8

The second differences are constant (both equal to 8), which suggests that the data can be modeled by a quadratic function.

Based on this analysis, the best model for the data is quadratic.