Question

The percentage of adult height attained by a girl who is x years old can be modeled byf(x)=63+36 log (x - 5)where x represents the girl's 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 12?A girl has attained% of her adult height by age 12.(Do not round until the final answer. Then round to the nearest tenth as needed.).

Answer 1

Given: The modlled equation below

$f(x)=63+36log(x-5)$

To Determine: The percentage at the age of 12

Solution

$\begin{gathered} f(x)=63+36log(x-5) \\ x=12 \\ f(x)=63+36log(12-5) \\ f(x)=63+36log7 \end{gathered}$$\begin{gathered} f(x)=63+36(0.845098) \\ f(x)=63+30.42 \\ f(x)=93.42 \\ f(x)\approx93.4(nearest-tenth) \end{gathered}$

Hence, a gril has attained 93.4 % of her adult height by age 12