Question

question 23, 7.6.35 part 2 of 4 growth of the human brain the data in the following table indicate that between the ages of 1 and 11, the human the graphing - calculator screen to the right displays the percentage of an adult brain complete parts (a) through (c) below. click the icon to view the table click the icon to view the scatter - plot a. explain why a logarithmic function was used to model the data. choose the correct a. the data increase at a steady rate b. the data increase rapidly and then continue to increase even more rapidly c. the data increase rapidly and then begin to decrease d. the data increase rapidly and then begin to level off b. use the graphing calculator screen to express the model in function notation, with f(x)= (type an expression using x as the variable.)

Explanation:

Logarithmic functions are often used to model data that increase rapidly at first and then level off. This is because the rate of growth of a logarithmic function slows down as the input variable increases. In the context of human - brain growth, it makes sense as the brain grows quickly in early childhood and then the growth rate slows as it approaches the adult size.

Answer:

a. D. The data increase rapidly and then begin to level off
b. Without seeing the actual graphing - calculator screen to determine the specific logarithmic model parameters, we cannot provide the function notation. If it were a general form of a common logarithmic function, it could be of the form \(f(x)=a + b\ln(x)\) or \(f(x)=a + b\log(x)\) (where \(a\) and \(b\) are constants determined by the data).