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

exponential
exponential

cubic
cubic

quadratic
quadratic

linear

Answer 1

To determine which type of function best models the data, let's analyze the growth values corresponding to the given days:

- 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.

First, we can calculate the differences between growth values to check for patterns:

1. **First Differences** (growth differences between consecutive days):
- Growth from day 1 to day 3: 12 - 0 = 12
- Growth from day 3 to day 5: 32 - 12 = 20
- Growth from day 5 to day 7: 60 - 32 = 28

First differences: 12, 20, 28

2. **Second Differences** (differences of the first differences):
- 20 - 12 = 8
- 28 - 20 = 8

Second differences: 8, 8

Since the second differences are constant, this indicates that the data can be modeled by a **quadratic function**.

Thus, the best type of function that models the given data is **quadratic**.