Chapter 4.4, Problem 68E

Brain Growth And IQs Refer to Exercise 67. The researchers at the Institute also measured the thickness (also in millimeters) of the cortex of children of age t years who were of average intelligence. These data lead to the model

A(t) = −0.00005t³ − 0.000826t² + 0.0153t + 4.55 (5 ≤ t ≤ 19)

Show that the cortex of children with average intelligence reaches maximum thickness at age 6 years.

Source: Nature.

67. Brain Growth And IQs In a study conducted at the National Institute of Mental Health, researchers followed the development of the cortex, the thinking part of the brain, in 307 children. Using repeated magnetic resonance imaging scans from childhood to the latter teens, they measured the thickness (in millimeters) of the cortex of children of age t years with the highest IQs−121 to 149. These data lead to the model

S(t) = 0.000989t³ − 0.0486t² + 0.7116t + 1.46 (5 ≤ t ≤ 19)

Show that the cortex of children with superior intelligence reaches maximum thickness around age 11 years.

Hint: Use the quadratic formula.

Source: Nature.