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2. Pediatricians monitor for normal growth of chidren by the annual measurement of height and weight. These are expected to increase annually, the growth curve paralleling a standardized curve. In the note introducing the idea of a derivative, there are data on juvenile heights from birth to age 18. Below is a table of both heights and weights for American girls in the 50^th percentile.

age(years)	height(cm)	weight(kg)
0	50	3.4
0.25	60	5.4
0.5	66	7.3
0.75	71	8.6
1	75	9.5
1.5	81	10.8
2	87	11.8
3	94	15.0
4	102	15.9
5	108	18.2
6	114	20.0
7	121	21.8
8	126	25.0
9	132	29.1
10	138	32.7
11	144	37.3
12	151	41.4
13	156	46.8
14	160	50.0
15	161	52.3
16	163	56.4
17	164	57.7
18	164	58.6

a. Use the data from ages 4 through 18, together with the trendline feature of Excel, to find a power law relationship between height and weight. Give a physiological explanation for this relationship.

b. Include the data back to birth (age 0). What happens to the power law? Why does this happen? (Think about the morphological changes between an infant and a small child.)

c. Create a graph of weight versus age, then create another graph of rate of change in weight versus age (much like the graphs seen in the notes). Recall that the rate of growth (in height) was relatively constant over the ages 3 to 12. What happens with the rate of change in weight? Describe the graph for the rate of weight gain over the early years (0-3), the ages 3-12, then adolescence (13-18).