Maximum Peak Age and Maximum Peak Velocity Trends from Adolescents through Functional Formula for Longitudinal Data by a Era from 1968 to 2019

Objectives The purpose of this study was to investigate changes in adolescents' physique using functional equations by utilizing longitudinal data from the Education Statistics Yearbook(2022) Methods Data processing for this study was done by modifying adolescents' physique (height, weight, BMI) growth data from the first grade of elementary school(6 years old) to the third grade of high school(17 years old) into longitudinal data to suit this study, and a total of 5 data were used. Divide into groups and use Origin Lab software to differentiate and fit functional equations suitable for the resulting values to determine Maximum Peak Age(MPA) and Maximum Peak Height(MPH), Maximum Peak Weight(MPW), Maximum Peak BMI(MPB), and Maximum Peak Velocity(MPV) were calculated and a growth curve graph was created, the significance level was set at .05 and presented as the explanatory power value. Results There was a significant difference in height changes between male and female adolescents from group 1 to group 5. In addition, it was found that there was a significant difference in weight change between groups 1 and 5 in both male and female adolescents. There was a significant difference in BMI changes between male and female adolescents from group 1 to group 5. Conclusions First, the group with the MPV rate of male students' height was group 4, the slowest group was group 1, and the MPV rate difference was 0.91 cm/v. Second, the group with the MPV rate of female students' height was group 4, the slowest group was group 2, and the MPV rate difference was 0.56 cm/v. Third, the group with the MPV rate of male body weight was group 2, and the group with the slowest was group 3, and the MPV rate difference was 0.49 kg/v. Fourth, the group with the MPV rate of female body weight was group 3, and the group with the slowest was group 5, and the difference in the MPV rate was 0.51 kg/v. Fifth, the group with the MPV rate of male BMI was group 3, the slowest group was group 5, and the maximum growth rate difference was 0.09 kg/m2/v. Sixth, the group with the MPV rate of female students' BMI was group 2, the slowest group was group 5, and the MPV rate difference was 0.34 kg/m2/v.