To determine which type of function best models the data provided, let's analyze the values:
- For day 1, growth is 0 inches.
- For day 3, growth is 12 inches.
- For day 5, growth is 32 inches.
- For day 7, growth is 60 inches.
First, let's look at the differences in the growth values:
-
From day 1 to day 3:
- Growth increases from 0 to 12 = 12 inches.
-
From day 3 to day 5:
- Growth increases from 12 to 32 = 20 inches.
-
From day 5 to day 7:
- Growth increases from 32 to 60 = 28 inches.
Next, let's calculate the first differences of the growth:
- First difference:
- From 0 to 12: 12
- From 12 to 32: 20
- From 32 to 60: 28
Now, calculate the second differences of the first differences:
- Second difference:
- From 12 to 20: 8
- From 20 to 28: 8
The second differences are constant (equal to 8), indicating that the growth of the function is quadratic. When the second differences are constant, this suggests a quadratic function is the best model.
So, the best option to model the data given in the table is:
quadratic.