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. 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 6? a child has □% of an adult size brain at age 6.

Explanation:

Step1: Identify the regression - model formula

The regression model is given by $y=a + b\ln x$, where $a = 28.82590162$ and $b = 30.43985983$.

Step2: Round the coefficients

Rounding $a\approx29$ and $b\approx30$.

Step3: Write the function in function - notation

The function is $f(x)=29 + 30\ln x$.

Step4: Calculate the value of the function at $x = 6$

Substitute $x = 6$ into $f(x)$: $f(6)=29+30\ln6$.
Since $\ln6\approx1.79176$, then $f(6)=29 + 30\times1.79176$.
$30\times1.79176 = 53.7528$, and $29+53.7528=82.7528\approx83$.

Answer:

b. $f(x)=29 + 30\ln x$
c. $83$