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.
(GRAPH CAN'T COPY)
The data for one of the two groups shown by the graphs can be modeled by
where $y$ is the head circumference, in centimeters, at age
$x$ months, $0 \leq x \leq 14$
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