Question

The table shows the average height, in centimeters, of a teenage girl at different ages. Does this data represent a linear or nonlinear function?


Age | 13 | 14 | 15 | 16 | 17 | 18
Height (cm) | 157 | 159 | 160 | 162 | 162 | 163

Answer 1

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.