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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

exponential
exponential

quadratic
quadratic

cubic
cubic

1 answer

To determine which type of function best models the given growth data, let's take a look at the provided values:

  • At 1 day, the growth is 0 inches.
  • At 3 days, the growth is 12 inches.
  • At 5 days, the growth is 32 inches.
  • At 7 days, the growth is 60 inches.

To analyze the growth, we can start calculating the differences in growth over time:

  1. Calculate the first differences (growth from day to day):

    • From day 1 to day 3: \( 12 - 0 = 12 \)
    • From day 3 to day 5: \( 32 - 12 = 20 \)
    • From day 5 to day 7: \( 60 - 32 = 28 \)

    So, the first differences are: 12, 20, 28.

  2. Calculate the second differences (difference of differences):

    • From 12 to 20: \( 20 - 12 = 8 \)
    • From 20 to 28: \( 28 - 20 = 8 \)

    The second differences are constant (both are 8).

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

Therefore, the best function type that models the given data is:

quadratic.