## Related questions with answers

Height velocity graphs are used by endocrinologists to follow the progress of children with growth deficiencies. The given figure shows the height velocity curves of an average boy and an average girl between ages 3 and 18.

(a) Which curve is for girls and which is for boys? Explain how you can tell.

(b) About how much does the average boy grow between ages 3 and 10 ?

(c) The growth spurt associated with adolescence and the onset of puberty occurs between ages 12 and 15 for the average boy and between ages 10 and 12.5 for the average girl. Estimate the height gained by each average child during this growth spurt.

(d) When fully grown, about how much taller is the average man than the average woman? (The average boy and girl are about the same height at age 3.)

Solution

Verifieda) The area under each curve represents the change in height in centimeters. Since men are generally taller than women, the curve with the larger area under it, is the height velocity of boys. Therefore, the black curve is for boys and the blue curve is for girls.

b) Each square of the grid has area $1 \text{ cm/yr} \cdot 1 \text{ yr} = 1 \text{ cm}$. Counting squares lying below the black curve in the interval $[3, 10]$ gives about 43 cm. Therefore, on average, between ages 3 and 10, boys grow about 43 cm.

c) Again, we need to count the squares lying below the blue curve in the interval $[10,12.5]$ and we find that on average, girls grow about 18 cm in their adolescence years. Similarly, we need to count the squares lying below the black curve in the interval $[12,15]$ and we find that on average, boys grow about 23 cm in their adolescence years.

d) We can measure the difference in growth by counting squares that lie between the two curves. In the interval $[3,12.5]$ the difference is about 5 cm in advantage for girls. In the interval $[12.5, 15]$ the difference is about 18 cm in advantage for boys. Therefore, when fully grown, the average man is about $18-5=13$ cm taller than the average woman.

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