Question

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

Time and Growth Data

Time (days) Growth (inches)
1
0
3
12
5
32
7
60
(1 point)
Responses

quadratic
quadratic

linear
linear

cubic
cubic

exponential

Answer 1

To determine which type of function best models the data provided, we need to analyze the growth values corresponding to the time values.

Here are the data points:

- At time 1 day, growth is 0 inches
- At time 3 days, growth is 12 inches
- At time 5 days, growth is 32 inches
- At time 7 days, growth is 60 inches

We can observe the growth is not linear because the differences between growth values are increasing rather than constant. Let's calculate the first and second differences:

- Growth differences:
- 12 - 0 = 12 (between 1 and 3)
- 32 - 12 = 20 (between 3 and 5)
- 60 - 32 = 28 (between 5 and 7)

The first differences are: 12, 20, 28

- Now, look at the second differences:
- 20 - 12 = 8
- 28 - 20 = 8

The second differences are constant (8), which suggests that the function modeling this data is likely a quadratic function.

Based on this analysis, the correct answer would be: **quadratic**.