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# team hw 2 - 5.3#36 a Which curve is for girls/boys How can...

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5.3 #36 a) Which curve is for girls/boys? How can you tell? a. The black curve represents boys. Boys generally hit puberty later, as known for common fact and stated in part c. Puberty is associated with a growth spurt, so we would expect the graph for boys do peak later than the one for girls. The black line peaks later and must therefore represent boys. b) How much does the average boy grow between 3 and 10? a. We are given a graph of the growth/year, but looking to find total growth. Instead of using the rate of change (growth/year), we need to use the integral to find total change (growth). As discussed in section 5.2, we know that the integral for a function is equal to the area between the graph of its derivative and the x axis for a given interval. Our interval is from 3 to 10, so we need to find the area under the given graph (derivative of total change.) Each square is equal to 1 cm/yr * 1 yr = 1 cm. We approximate how many total squares there are under the black curve between 3 and 10 years and got approximately 42.25 cm c) Estimate height gained by each child during their growth spurt a. We already discussed how to find total growth for a period in part b, so now we just do this again for both curves using different intervals. For girls, we take the area under their curve from 10 to 12.5 and for boys we take the area from 12 to 15. After counting up approximate area, we came to the answer of approximately 23 cm growth for boys and approximately 18cm growth for girls during their growth spurts.

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