Question

the percentage of adult height attained by a girl who is x years old can be modeled by
f(x)=62 + 35 log(x - 4)
where x represents the girls age (from 5 to 15) and f(x) represents the percentage of her adult height. complete parts (a) and (b) below.
a. according to the model, what percentage of her adult height has a girl attained at age 13?
a girl has attained % of her adult height by age 13.
(do not round until the final answer. then round to the nearest tenth as needed.)

Explanation:

Step1: Substitute \(x = 13\) into the function

Given \(f(x)=62 + 35\log(x - 4)\), when \(x = 13\), we have \(f(13)=62+35\log(13 - 4)\).
Since \(13-4 = 9\), then \(f(13)=62+35\log(9)\).

Step2: Calculate the value of \(\log(9)\)

We know that \(\log(9)\approx0.9542425094\) (using the common logarithm, \(\log_{10}(9)\)).

Step3: Calculate \(35\log(9)\)

\(35\times0.9542425094=33.49848733\).

Step4: Calculate \(f(13)\)

\(f(13)=62 + 33.49848733=95.49848733\).

Answer:

\(95.5\)