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

cubic
cubic

exponential
exponential

linear
linear

quadratic
quadratic

Answer 1

To determine which type of function best models the given data, let's analyze the growth pattern based on the time and growth data provided.

The data points are as follows:

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

We can look for a pattern:

1. **Calculate the first differences** (the difference in growth between consecutive days):
- From 0 to 12 (at 3 days): 12 - 0 = 12
- From 12 to 32 (at 5 days): 32 - 12 = 20
- From 32 to 60 (at 7 days): 60 - 32 = 28

First differences: 12, 20, 28

2. **Calculate the second differences** (the difference between the first differences):
- From 12 to 20: 20 - 12 = 8
- From 20 to 28: 28 - 20 = 8

Second differences: 8, 8

The second differences are constant, indicating that the growth can be modeled by a **quadratic function**. Linear functions would show constant first differences, and cubic or exponential functions would behave differently.

Therefore, the best type of function to model the given data is **quadratic**.