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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

quadratic
quadratic

exponential
exponential

cubic
cubic

linear
linear
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1 answer

To determine the best type of function that models the data in the table, let's look closely at the growth pattern over time. We have the following data points:

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

To analyze the growth, we can find the differences in growth values for each interval:

  1. From Day 1 to Day 3: Growth went from 0 to 12 inches (change = 12).
  2. From Day 3 to Day 5: Growth went from 12 to 32 inches (change = 20).
  3. From Day 5 to Day 7: Growth went from 32 to 60 inches (change = 28).

Next, we look at the differences of the differences (second differences):

  1. From Day 1 to Day 3 to Day 5: 20 - 12 = 8
  2. From Day 3 to Day 5 to Day 7: 28 - 20 = 8

Since the second differences are constant (8), this indicates that the data is best modeled by a quadratic function.

Therefore, the correct response is:

quadratic