the data in the following table indicate that between the ages of 1 and 11, the human brain does not grow…

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 scatter - plot. 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 level off. d. the data increase rapidly and then begin to decrease. 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.) c. according to the model in part (b), what percentage of an adult size brain does a child have at age 10? a child has □% of an adult size brain at age 10

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 scatter - plot. 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 level off. d. the data increase rapidly and then begin to decrease. 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.) c. according to the model in part (b), what percentage of an adult size brain does a child have at age 10? a child has □% of an adult size brain at age 10

Answer

Explanation:

Step1: Understand logarithmic - function behavior

Logarithmic functions are used when data increases rapidly at first and then levels off. This is because the rate of change of a logarithmic function $y = a + b\ln x$ decreases as $x$ increases.

Step2: Answer part (a)

The correct reason for using a logarithmic function is that the data increase rapidly and then begin to level off. So the answer for part (a) is C.

Step3: Write the function for part (b)

Given $y=a + b\ln x$ with $a = 29.68705354\approx30$ and $b = 30.06167779\approx30$, the function in function - notation is $f(x)=30 + 30\ln x$.

Step4: Solve part (c)

Substitute $x = 10$ into $f(x)=30 + 30\ln x$. We know that $\ln10\approx2.3026$. Then $f(10)=30+30\times2.3026=30 + 69.078\approx99$.

Answer:

a. C. The data increase rapidly and then begin to level off. b. $f(x)=30 + 30\ln x$ c. 99