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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

linear
linear

quadratic
quadratic

cubic
cubic

exponential

1 answer

To determine which type of function best models the provided data, we can analyze the growth in relation to time. Here's the data presented clearly:

  • Time (days): 1, 3, 5, 7
  • Growth (inches): 0, 12, 32, 60

Now let's observe the change in growth between time intervals:

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

Now let's look at the second differences:

  • First differences: 12, 20, 28
  • Second differences: 20 - 12 = 8, 28 - 20 = 8

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

Therefore, the best choice that models the data is:

Quadratic.