Question

the data in the following table indicate that between the ages of 1 and 11, the human brain does not grow linearly, or steadily. a scatter plot for the data is shown below the table. the graphing calculator screen to the right displays the percentage of an adult brain, y, for a child at age x, where 1 ≤ x ≤ 11. use this information to complete parts (a) through (c) below. click the icon to view the table. click the icon to view the scatterplot. a. explain why a logarithmic function was used to model the data. choose the correct answer below. a. the data increase rapidly and then begin to level off. b. the data increase rapidly and then begin to decrease. c. the data increase rapidly and then continue to increase even more rapidly.

Explanation:

Logarithmic functions \(y = a + b\ln x\) have a characteristic shape where the function increases rapidly at first and then levels off as \(x\) gets larger. This behavior matches the description of the data (the human brain growth between ages 1 and 11 not being linear). Option B is incorrect because the data is about growth (so not decreasing). Option C is incorrect because logarithmic functions do not show an acceleration in growth (they level off), while option A correctly describes the behavior of a logarithmic function (rapid increase followed by leveling - off).

Answer:

A. The data increase rapidly and then begin to level off.