The BMI is usually used as a guideline to determine whether a person is overweight or underweight. For example, according to the Centers for Disease Control, a 12-year-old boy is at risk of being overweight if his BMI is between 21 and 24 and is considered overweight if his BMI is above 24. A 13-year-old boy is at risk of being overweight if his BMI is between 22 and 25 and is overweight if his BMI is above 25.

(a) At age 12, a boy’s weight was 50 kilograms and his height was 1.55 meters. Find his BMI and determine whether he is overweight or at risk of being overweight. 

(b) Suppose that the boy’s weight was increasing at the rate of 7 kilograms per year and his height was increasing at the rate of 5 centimeters per year. Find the rate of change of his BMI at age 12 or b(12).

(c) Use the values b(12) and b(12) to estimate b(13), the BMI of the child at age 13. Is the child at risk of being overweight when he turns 13?