Answer
See below:
Work Step by Step
\[\left( \text{a} \right)\]
In the calculator with an LOG key, put \[x=13\] in the given equation \[f\left( x \right)=62+35\log \left( x-4 \right)\], and simplify it up to the nearest tenth of a percent.
\[\begin{align}
& f\left( 13 \right)=62+35\log \left( 13-4 \right) \\
& =62+35\times 2\log 3 \\
\end{align}\]
The value of \[f\left( 13 \right)\] comes out to be \[\left( 95.3985 \right)\].
Round off this value to the nearest tenth of a percent to get the answer as \[95.4\] percent.
The percentage of the adult height a girl has attained at age 13 is \[95.4\] percent.
\[\left( \text{b} \right)\]
In this case, the growth of a girl is being modeled. A girl usually grows from 5 to 15 years. Hence, both of these are included in the model. Also, as the rate of growth is very high in the initial ages, that is when the girl is young and is slower when the girl is a teenager, hence the logarithmic function is a good method of modeling this situation.
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