If human height were quantized in 1 -cm 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 increase, (iii) the child's height would increase in jumps of \(6 \mathrm{~cm}\), or (iv) the child's height would increase in "jumps" of \(1 \mathrm{~cm}\) at a time?

If human height is quantized in 1-cm increments, this means that the height can only increase in discrete steps of 1 cm. In other words, an individual's height can only be an integer multiple of 1 centimeter (e.g. not \({245.5 cm}\), but only \({245 cm}\) or \({246 cm}\)).

Now let's examine the given options one by one and determine which one describes the growth pattern of a child according to the quantized height in 1-cm increments: (i) If "the child's height would never change," this would mean the child would not grow at all, which is unrealistic. (ii) "The child's height would continuously increase" implies that growth is constantly happening, as in a smooth, continuous manner. However, this doesn't match with the concept of quantized height in 1-cm increments, which involves discrete, step-by-step growth. (iii) While "the child's height would increase in jumps of 6 cm" involves distinct increases in height, it doesn't match the given scenario of human height being quantized in 1-cm increments. (iv) "The child's height would increase in 'jumps' of 1 cm at a time" is consistent with the concept of quantized height in 1-cm increments, as the child's height would increase in discrete steps of 1 cm.

Based on our analysis, the best possible option that describes the growth pattern of a child when human height is quantized in 1-cm increments is: (iv) the child's height would increase in "jumps" of 1 cm at a time.