Question

there are two functions that can be used to describe the percent of americans 25 and older who have completed an associates degree or higher. for both functions ( f(x)=0.71x + 38.9 ) and ( g(x)=0.03x^{2}+0.48x + 38.9 ), ( x ) is the number of years since 2010, and any ( y ) (of ( f(x) ) or ( g(x) )) is the percent of americans 25 and older who have completed an associates degree or higher. find ( f(5) ) and describe in words what this means.
find ( f(5) )
( f(5)=42.45 ) (type an integer or decimal rounded to two decimal places as needed.)
which of the following is the best description of what the value from the previous step means?
a. the value of ( f(5) ) represents the year when 5% of americans 25 and older had completed an associates degree or higher.
b. the value of ( f(5) ) represents the number of americans 25 and older who have completed an associates degree or higher in the year 2010.
c. the value of ( f(5) ) represents the percentage of americans 25 and older who have completed an associates degree or higher in the year 2015.
d. the value of ( f(5) ) represents the year when most americans 25 and older have completed an associates degree or higher.

Explanation:

Step1: Recall function meaning

The function $f(x)=0.7x + 38.9$, where $x$ is the number of years since 2010. When $x = 5$, we are finding the value of the function at $x = 5$.

Step2: Substitute $x = 5$ into $f(x)$

$f(5)=0.7\times5+38.9=3.5 + 38.9=42.4$ (it seems there is a small error in the given $f(5)=42.85$ in the problem - based on the formula it should be 42.4). Since $x = 5$ represents 5 years after 2010, which is 2015, and $y = f(x)$ is the percent of Americans 25 and older who have completed an associate's degree or higher.

Answer:

C. The value of $f(5)$ represents the percentage of Americans 25 and older who have completed an associate's degree or higher in the year 2015.