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 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 numbers rounded to the nearest whole number.
f(x)=□
(type an expression using x as the variable.)

Explanation:

a. Logarithmic functions are often used when data initially increases rapidly and then levels off. This is because the rate of growth of a logarithmic function slows down as the input variable increases.
b. Given the regression equation $y = a + b\ln x$ with $a = 29.75918143$ and $b = 29.92038797$, rounding to the nearest whole - number, $a\approx30$ and $b\approx30$. So the function notation is $f(x)=30 + 30\ln x$.

Answer:

a. D. The data increase rapidly and then begin to level off.
b. $f(x)=30 + 30\ln x$