If human height were quantized in 1 -foot increments, what would happen to the height of a child as she grows up: (i) The child's height would never change, (ii) the child's height would continuously get greater, (iii) the child's height would increase in "jumps" of 1 foot at a time, or (iv) the child's height would increase in jumps of 6 inches?

Quantization is the process of converting continuous values or signals into discrete values. In this exercise, human height is quantized in 1-foot increments, meaning that height can only be represented as whole feet (e.g., 4 feet, 5 feet, 6 feet, etc.) and not any values in between (e.g. 4.5 feet, 5.75 feet, etc).

Since height is quantized in 1-foot increments, as the child grows, her height would only increase when she attains each whole feet value. It would not change at any values between those whole feet increments.

Based on our understanding of quantization and how it affects the child's growth, let's evaluate each option: (i) The child's height would never change: This is incorrect, as the child's height would change when she reaches the next whole feet increment. (ii) The child's height would continuously get greater: This is also incorrect, as the child's height would not change continuously but would increase only when the next 1-foot increment is obtained. (iii) The child's height would increase in "jumps" of 1 foot at a time: This is the correct option, as the height would increase only when the child achieves each 1-foot increment. (iv) The child's height would increase in jumps of 6 inches: This is incorrect, as the height is quantized in 1-foot increments, not 6-inch increments. So the correct answer is (iii) the child's height would increase in "jumps" of 1 foot at a time.