To determine whether the data represents a linear or nonlinear function, we can analyze the relationship between age and height. A linear function would show a constant rate of change (slope) between the age and height, while a nonlinear function would exhibit changes in the rate of growth.
Let's look at the changes in height from one age to the next:
- From age 13 to 14: Height increases from 157 cm to 159 cm (Change = 2 cm)
- From age 14 to 15: Height increases from 159 cm to 160 cm (Change = 1 cm)
- From age 15 to 16: Height increases from 160 cm to 162 cm (Change = 2 cm)
- From age 16 to 17: Height remains the same (Change = 0 cm)
- From age 17 to 18: Height increases from 162 cm to 163 cm (Change = 1 cm)
The height changes are: 2 cm, 1 cm, 2 cm, 0 cm, 1 cm.
Since the changes in height are not constant (they vary from age to age), this indicates a nonlinear relationship between age and height. The growth does not occur at a steady rate, hence this data represents a nonlinear function.
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