Chapter 8.1, Problem 89ES

Autism is a neurological disorder that impedes language and derails social and emotional development. New findings suggest that the condition is not a sudden calamity that strikes children at the age of 2 or 3, but a developmental problem linked to abnormally rapid brain growth during infancy. The graphs show that the heads of severely autistic children start out smaller than average and then go through a period of explosive growth. Exercises 89 -90 involve mathematical models for the data shown by the graphs.

89 The data for one of me two groups shown by the graphs can be modeled by $y=2.9\sqrt{x}+36$
where y is the head circumference, in centimeters, at age x months, $0\le x\le 14$
a. According to the model what is the head circumference at birth.
b. According to the model what is the head circumference at 9 months.
c. According to the model, what is the head circumference at 14 months? Use a calculator and round to the nearest tenth of a centimeter.
d. Use the values that you obtained in parts (a) through (c) and the graphs shown above to determine if the given model describes healthy children or severe autistics.