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 ( 1leq xleq11 ). use this information to complete parts (a) through (c) below

click the icon to view the table

click the icon to view the scatterplot

( f(x)=32 + 29ln 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 (square%) 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

Explanation:

Step1: Substitute \(x = 10\) into the function

We have the function \(f(x)=32 + 29\ln x\). Substitute \(x = 10\) into it: \(f(10)=32+29\ln(10)\)

Step2: Calculate \(\ln(10)\) and then the value of \(f(10)\)

We know that \(\ln(10)\approx2.3026\). Then \(f(10)=32 + 29\times2.3026\)

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Step3: Round the result

Rounding \(98.7754\) to the nearest whole number gives \(99\)

Answer:

A child has \(99\%\) of an adult - size brain at age 10.