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)=30 + 30 ln 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 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 overestimates the percent displayed by the table by % b. the model underestimates the percent displayed by the table by %

Explanation:

Step1: Recall the function from part (b)

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

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: Compare with table value

We don't know the table - value. But assume the table - value is $t$. If $t<99$, the model overestimates by $99 - t$. If $t > 99$, the model underestimates by $t - 99$.

Answer:

We need the value from the table to determine if it overestimates or underestimates and by how much. If the table value is $t$:
If $t<99$, A. The model overestimates the percent displayed by the table by $(99 - t)\%$.
If $t>99$, B. The model underestimates the percent displayed by the table by $(t - 99)\%$.