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)=0.78x + 32.4) and (g(x)=0.03x^{2}+0.46x + 32.6), (x) is the number of years since 2010, and any (y) (or (f(x)) or (g(x))) is the percent of americans 25 and older who have completed an associates degree or higher. find (f(2)) and describe in words what this means.
find (f(2))
f(2)=33.96
(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(2)) represents the year when 2% of americans 25 and older had completed an associates degree or higher.
b. the value of (f(2)) represents the year when most americans 25 and older have completed an associates degree or higher.
c. the value of (f(2)) represents the percentage of americans 25 and older who have completed an associates degree or higher in the year 2012.
d. the value of (f(2)) represents the number of americans 25 and older who have completed an associates degree or higher in the year 2010.

Explanation:

Step1: Identify the function to evaluate

We are given \(f(x)=0.78x + 32.4\) and we need to find \(f(2)\).

Step2: Substitute \(x = 2\) into the function

Substitute \(x=2\) into \(f(x)=0.78x + 32.4\), we get \(f(2)=0.78\times2+32.4\).

Step3: Perform the calculations

First, calculate \(0.78\times2 = 1.56\). Then \(1.56+32.4=33.96\).

Step4: Interpret the result

Since \(x\) is the number of years since 2010, when \(x = 2\), it represents the year 2012. And \(y = f(x)\) is the percent of Americans 25 and older who have completed an associate - degree or higher. So \(f(2)\) represents the percentage of Americans 25 and older who have completed an associate's degree or higher in the year 2012.

Answer:

\(f(2)=33.96\)
C. The value of \(f(2)\) represents the percentage of Americans 25 and older who have completed an associate's degree or higher in the year 2012.