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

exponential
exponential

linear
linear

cubic
cubic
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Answer 1

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

The data you've provided is:

- At 1 day: 0 inches
- At 3 days: 12 inches
- At 5 days: 32 inches
- At 7 days: 60 inches

### Growth Differences
First, let's look at the differences in growth:

- From day 1 to day 3: 12 - 0 = 12 inches
- From day 3 to day 5: 32 - 12 = 20 inches
- From day 5 to day 7: 60 - 32 = 28 inches

These first differences (12, 20, 28) are not constant, suggesting that the growth is not linear.

### Second Differences
Next, let's find the second differences:

- From 12 to 20: 20 - 12 = 8
- From 20 to 28: 28 - 20 = 8

The second differences are constant (8), indicating that the data can be modeled by a quadratic function.

### Conclusion
From this analysis, the best conclusion is that the data is best modeled by a **quadratic function**.