Question

the percentage of adult height attained by a girl who is x years old can be modeled by f(x)=63 + 35 log(x - 3) 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 12? a girl has attained 96.4% of her adult height by age 12 (do not round until the final answer. then round to the nearest tenth as needed.) b. why was a logarithmic function used to model the percentage of adult height attained by a girl from ages 5 to 15, inclusive? a. height increases at a steady rate, regardless of ones age b. height increases rapidly at a young age, and continues to increase even faster as one gets older c. height increases rapidly at a young age, and then increases more slowly d. height increases rapidly at a young age, stops increasing at a certain age, and then starts decreasing

Explanation:

Step1: Substitute x = 12 into the function

$f(12)=63 + 35\log(12 - 3)$
$=63+35\log(9)$

Step2: Calculate the value of $\log(9)$ and the function

We know that $\log(9)\approx0.9542425094$. Then $35\log(9)\approx35\times0.9542425094 = 33.39848783$. And $63+33.39848783=96.39848783\approx96.4$

Step3: Answer part (b)

The reason a logarithmic function is used is that height increases rapidly at a young age, and then increases more slowly. Logarithmic functions have a property of starting with a rapid - change rate and then the rate of change slows down.

Answer:

a. 96.4
b. C. Height increases rapidly at a young age, and then increases more slowly.