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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

exponential
exponential

cubic
cubic

1 answer

To determine which type of function best models the data given in the table (Time vs. Growth), we can examine how the growth values change as time increases.

Here are the data points you provided:

  • At Day 1, Growth = 0 inches
  • At Day 3, Growth = 12 inches
  • At Day 5, Growth = 32 inches
  • At Day 7, Growth = 60 inches

Next, we can examine the difference between the growth values at different time points to identify a pattern:

  1. Growth from Day 1 to Day 3: 12 - 0 = 12 inches
  2. Growth from Day 3 to Day 5: 32 - 12 = 20 inches
  3. Growth from Day 5 to Day 7: 60 - 32 = 28 inches

Now, let's look at the differences of these differences:

  1. From 12 to 20: 20 - 12 = 8
  2. From 20 to 28: 28 - 20 = 8

Since the second differences are constant (both equal to 8), this suggests that the growth of the data can be modeled by a quadratic function.

Thus, the best model for the data in the table is:

Quadratic