Question

the data in the following table indicates 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)=30 + 30lnx (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 99% of an adult size brain at age 10 (round to the nearest whole number as needed.) does this overestimate or underestimate the percent displayed by the table? by how much? select the correct choice below and fill in the answer box within your choice. a. the model underestimates the percent displayed by the table by % b. the model overestimates the percent displayed by the table by %

Explanation:

Step1: Recall the model function

$f(x)=30 + 30\ln x$

Step2: Substitute $x = 10$ into the function

$f(10)=30+30\ln(10)$
Since $\ln(10)\approx2.3026$, then $f(10)=30 + 30\times2.3026=30+69.078 = 99.078\approx99$

Step3: Analyze over - or under - estimation

We need to know the value from the table (not given here). But if we assume the value from the table is $v$.
If $v>99$, the model underestimates. If $v < 99$, the model overestimates.
Let's assume we find from the table the value is $95$ (for illustration purposes as the table is not shown).
The difference is $99 - 95=4$. So the model overestimates.

Answer:

If the value from the table is lower than 99, the answer is B. The model overestimates the percent displayed by the table by <difference in percentage points>. If the value from the table is higher than 99, the answer is A. The model underestimates the percent displayed by the table by <difference in percentage points>.