Answer
,
Work Step by Step
(a)
From the graph it can be observed that the data points in the graph are increasing, although the rate of increase is slowing down. As the age the individual increases, the growth rate does not increase rapidly as it increased earlier.
Hence, to depict this behavior of the growth of the brain of an individual, the logarithmic plot is preferred.
The logarithmic function has to be used to model the growth of the human brain data provided in graph.
(b)
Follow the below-mentioned steps in TI83 to express the model in function notation.
Step 1. Hit the Y= key and turn off any equations.
Step 2. Hit the STAT key.
Step 3. Select 1: Edit.
Step 4. Under L1, type in the x¬-values.
Step 5. Under L2, type in the y-values.
Step 6. Hit the STAT key. Use the right arrow to get into the CALC options. Under CALC, choose option 9, that is LNREG.
Step 7. Enter the syntax in the form:
LNREG [x-list, y-list, frequency, equation].
Now, the model is obtained as:
$y=32+29\left( \ln \,x \right)$
(c)
$y=31.945+28.947\left( \ln x \right)$ ….. (1)
Put the value of\[x=8\].
Solve for y, we get
\[\begin{align}
& y=31.954+60.19359 \\
& =92.14759 \\
& \approx 92
\end{align}\]
The estimation is same as the percentage of growth of the human brain percent displayed in the table.
